id sid tid token lemma pos bibechana-46416 1 1 bibechana bibechana PROPN bibechana-46416 1 2 19(1 19(1 NUM bibechana-46416 1 3 - - SYM bibechana-46416 1 4 2 2 NUM bibechana-46416 1 5 ) ) PUNCT bibechana-46416 1 6 ( ( PUNCT bibechana-46416 1 7 2022 2022 NUM bibechana-46416 1 8 ) ) PUNCT bibechana-46416 1 9 165 165 NUM bibechana-46416 1 10 - - SYM bibechana-46416 1 11 169 169 NUM bibechana-46416 1 12 165 165 NUM bibechana-46416 1 13 165 165 NUM bibechana-46416 1 14 energy energy NOUN bibechana-46416 1 15 eigenvalue eigenvalue NOUN bibechana-46416 1 16 and and CCONJ bibechana-46416 1 17 thermodynamic thermodynamic ADJ bibechana-46416 1 18 properties property NOUN bibechana-46416 1 19 of of ADP bibechana-46416 1 20 qdeformed qdeformed ADJ bibechana-46416 1 21 hulthen hulthen ADJ bibechana-46416 1 22 potential potential ADJ bibechana-46416 1 23 1*bhishma 1*bhishma PROPN bibechana-46416 1 24 karki karki NOUN bibechana-46416 1 25 , , PUNCT bibechana-46416 1 26 2 2 NUM bibechana-46416 1 27 , , PUNCT bibechana-46416 1 28 3 3 NUM bibechana-46416 1 29 , , PUNCT bibechana-46416 1 30 4saddam 4saddam PROPN bibechana-46416 1 31 husain husain NOUN bibechana-46416 1 32 dhobi dhobi PROPN bibechana-46416 1 33 , , PUNCT bibechana-46416 1 34 2 2 NUM bibechana-46416 1 35 , , PUNCT bibechana-46416 1 36 4jeevan 4jeevan PROPN bibechana-46416 1 37 jyoti jyoti PROPN bibechana-46416 1 38 nakarmi nakarmi PROPN bibechana-46416 1 39 , , PUNCT bibechana-46416 1 40 2,4kishori 2,4kishori NUM bibechana-46416 1 41 yadav yadav NOUN bibechana-46416 1 42 1*department 1*department NUM bibechana-46416 1 43 of of ADP bibechana-46416 1 44 physics physics PROPN bibechana-46416 1 45 , , PUNCT bibechana-46416 1 46 tri tri PROPN bibechana-46416 1 47 - - ADJ bibechana-46416 1 48 chandra chandra PROPN bibechana-46416 1 49 multiple multiple ADJ bibechana-46416 1 50 campus campus PROPN bibechana-46416 1 51 , , PUNCT bibechana-46416 1 52 tribhuvan tribhuvan PROPN bibechana-46416 1 53 university university PROPN bibechana-46416 1 54 , , PUNCT bibechana-46416 1 55 kathmandu-44600 kathmandu-44600 NOUN bibechana-46416 1 56 , , PUNCT bibechana-46416 1 57 nepal nepal NOUN bibechana-46416 1 58 2department 2department NUM bibechana-46416 1 59 of of ADP bibechana-46416 1 60 physics physics PROPN bibechana-46416 1 61 , , PUNCT bibechana-46416 1 62 patan patan ADJ bibechana-46416 1 63 multiple multiple ADJ bibechana-46416 1 64 campus campus PROPN bibechana-46416 1 65 , , PUNCT bibechana-46416 1 66 tribhuvan tribhuvan PROPN bibechana-46416 1 67 university university PROPN bibechana-46416 1 68 , , PUNCT bibechana-46416 1 69 lalitpur-44700 lalitpur-44700 NOUN bibechana-46416 1 70 , , PUNCT bibechana-46416 1 71 nepal nepal ADJ bibechana-46416 1 72 3robotics 3robotics NUM bibechana-46416 1 73 academy academy NOUN bibechana-46416 1 74 of of ADP bibechana-46416 1 75 nepal nepal ADJ bibechana-46416 1 76 , , PUNCT bibechana-46416 1 77 lalitpur-44700 lalitpur-44700 NOUN bibechana-46416 1 78 , , PUNCT bibechana-46416 1 79 nepal nepal ADJ bibechana-46416 1 80 4innovative 4innovative NUM bibechana-46416 1 81 ghar ghar NOUN bibechana-46416 1 82 nepal nepal ADJ bibechana-46416 1 83 , , PUNCT bibechana-46416 1 84 lalitpur-44700 lalitpur-44700 NOUN bibechana-46416 1 85 , , PUNCT bibechana-46416 1 86 nepal nepal NOUN bibechana-46416 1 87 * * PUNCT bibechana-46416 1 88 corresponding correspond VERB bibechana-46416 1 89 author author NOUN bibechana-46416 1 90 email email NOUN bibechana-46416 1 91 : : PUNCT bibechana-46416 1 92 magnum.photon@gmail.com magnum.photon@gmail.com X bibechana-46416 1 93 article article NOUN bibechana-46416 1 94 information information NOUN bibechana-46416 1 95 : : PUNCT bibechana-46416 1 96 received receive VERB bibechana-46416 1 97 : : PUNCT bibechana-46416 1 98 july july PROPN bibechana-46416 1 99 28 28 NUM bibechana-46416 1 100 , , PUNCT bibechana-46416 1 101 2021 2021 NUM bibechana-46416 1 102 accepted accept VERB bibechana-46416 1 103 : : PUNCT bibechana-46416 1 104 february february PROPN bibechana-46416 1 105 26 26 NUM bibechana-46416 1 106 , , PUNCT bibechana-46416 1 107 2022 2022 NUM bibechana-46416 1 108 keywords keyword NOUN bibechana-46416 1 109 : : PUNCT bibechana-46416 1 110 gaussian gaussian ADJ bibechana-46416 1 111 hypergeometric hypergeometric ADJ bibechana-46416 1 112 function function NOUN bibechana-46416 1 113 thermodynamic thermodynamic ADJ bibechana-46416 1 114 properties property NOUN bibechana-46416 1 115 partition partition NOUN bibechana-46416 1 116 function function VERB bibechana-46416 1 117 nuclear nuclear ADJ bibechana-46416 1 118 physics physics PROPN bibechana-46416 1 119 abstract abstract NOUN bibechana-46416 1 120 the the DET bibechana-46416 1 121 objective objective NOUN bibechana-46416 1 122 of of ADP bibechana-46416 1 123 this this DET bibechana-46416 1 124 work work NOUN bibechana-46416 1 125 is be AUX bibechana-46416 1 126 to to PART bibechana-46416 1 127 calculate calculate VERB bibechana-46416 1 128 the the DET bibechana-46416 1 129 energy energy NOUN bibechana-46416 1 130 eigenvalue eigenvalue NOUN bibechana-46416 1 131 for for ADP bibechana-46416 1 132 q q ADV bibechana-46416 1 133 - - PUNCT bibechana-46416 1 134 deformed deform VERB bibechana-46416 1 135 hulthen hulthen NOUN bibechana-46416 1 136 potential potential NOUN bibechana-46416 1 137 using use VERB bibechana-46416 1 138 a a DET bibechana-46416 1 139 gaussian gaussian ADJ bibechana-46416 1 140 hypergeometric hypergeometric ADJ bibechana-46416 1 141 function function NOUN bibechana-46416 1 142 with with ADP bibechana-46416 1 143 centrifugal centrifugal ADJ bibechana-46416 1 144 approximation approximation NOUN bibechana-46416 1 145 factor factor NOUN bibechana-46416 1 146 and and CCONJ bibechana-46416 1 147 related relate VERB bibechana-46416 1 148 thermodynamical thermodynamical ADJ bibechana-46416 1 149 properties property NOUN bibechana-46416 1 150 . . PUNCT bibechana-46416 2 1 for for ADP bibechana-46416 2 2 this this PRON bibechana-46416 2 3 , , PUNCT bibechana-46416 2 4 we we PRON bibechana-46416 2 5 develop develop VERB bibechana-46416 2 6 a a DET bibechana-46416 2 7 mathematical mathematical ADJ bibechana-46416 2 8 model model NOUN bibechana-46416 2 9 using use VERB bibechana-46416 2 10 the the DET bibechana-46416 2 11 schrodinger schrodinger PROPN bibechana-46416 2 12 wave wave NOUN bibechana-46416 2 13 equation equation NOUN bibechana-46416 2 14 to to PART bibechana-46416 2 15 find find VERB bibechana-46416 2 16 the the DET bibechana-46416 2 17 energy energy NOUN bibechana-46416 2 18 eigenvalue eigenvalue NOUN bibechana-46416 2 19 . . PUNCT bibechana-46416 3 1 in in ADP bibechana-46416 3 2 addition addition NOUN bibechana-46416 3 3 , , PUNCT bibechana-46416 3 4 the the DET bibechana-46416 3 5 thermodynamic thermodynamic ADJ bibechana-46416 3 6 parameters parameter NOUN bibechana-46416 3 7 were be AUX bibechana-46416 3 8 also also ADV bibechana-46416 3 9 calculated calculate VERB bibechana-46416 3 10 for for ADP bibechana-46416 3 11 q q ADV bibechana-46416 3 12 - - PUNCT bibechana-46416 3 13 deformed deform VERB bibechana-46416 3 14 hulthen hulthen NOUN bibechana-46416 3 15 potential potential NOUN bibechana-46416 3 16 using use VERB bibechana-46416 3 17 the the DET bibechana-46416 3 18 partition partition NOUN bibechana-46416 3 19 function function NOUN bibechana-46416 3 20 . . PUNCT bibechana-46416 4 1 the the DET bibechana-46416 4 2 energy energy NOUN bibechana-46416 4 3 eigenvalue eigenvalue PROPN bibechana-46416 4 4 for for ADP bibechana-46416 4 5 quantum quantum NOUN bibechana-46416 4 6 numbers number NOUN bibechana-46416 4 7 n=1 n=1 PROPN bibechana-46416 4 8 to to ADP bibechana-46416 4 9 n=5 n=5 PROPN bibechana-46416 4 10 was be AUX bibechana-46416 4 11 observed observe VERB bibechana-46416 4 12 for for ADP bibechana-46416 4 13 screening screen VERB bibechana-46416 4 14 parameters parameter NOUN bibechana-46416 4 15 0.1 0.1 NUM bibechana-46416 4 16 , , PUNCT bibechana-46416 4 17 0.5 0.5 NUM bibechana-46416 4 18 , , PUNCT bibechana-46416 4 19 and and CCONJ bibechana-46416 4 20 1 1 X bibechana-46416 4 21 . . X bibechana-46416 5 1 in in ADP bibechana-46416 5 2 between between ADP bibechana-46416 5 3 , , PUNCT bibechana-46416 5 4 0.1 0.1 NUM bibechana-46416 5 5 to to PART bibechana-46416 5 6 1 1 NUM bibechana-46416 5 7 and and CCONJ bibechana-46416 5 8 n=1 n=1 PROPN bibechana-46416 5 9 to to PART bibechana-46416 5 10 n=2 n=2 ADV bibechana-46416 5 11 the the DET bibechana-46416 5 12 energy energy NOUN bibechana-46416 5 13 eigenvalue eigenvalue NOUN bibechana-46416 5 14 ranges range VERB bibechana-46416 5 15 from from ADP bibechana-46416 5 16 -1.048 -1.048 NOUN bibechana-46416 5 17 to to ADP bibechana-46416 5 18 -208.572 -208.572 PROPN bibechana-46416 5 19 . . PUNCT bibechana-46416 6 1 the the DET bibechana-46416 6 2 energy energy NOUN bibechana-46416 6 3 eigenvalue eigenvalue NOUN bibechana-46416 6 4 for for ADP bibechana-46416 6 5 considering consider VERB bibechana-46416 6 6 potential potential ADJ bibechana-46416 6 7 shows show NOUN bibechana-46416 6 8 that that PRON bibechana-46416 6 9 decrease decrease VERB bibechana-46416 6 10 with with ADP bibechana-46416 6 11 increasing increase VERB bibechana-46416 6 12 the the DET bibechana-46416 6 13 quantum quantum ADJ bibechana-46416 6 14 number number NOUN bibechana-46416 6 15 which which PRON bibechana-46416 6 16 means mean VERB bibechana-46416 6 17 electron electron NOUN bibechana-46416 6 18 are be AUX bibechana-46416 6 19 loosely loosely ADV bibechana-46416 6 20 bounded bound VERB bibechana-46416 6 21 nucleus nucleus NOUN bibechana-46416 6 22 in in ADP bibechana-46416 6 23 an an DET bibechana-46416 6 24 atom atom NOUN bibechana-46416 6 25 . . PUNCT bibechana-46416 7 1 also also ADV bibechana-46416 7 2 , , PUNCT bibechana-46416 7 3 the the DET bibechana-46416 7 4 vibrational vibrational ADJ bibechana-46416 7 5 mean mean NOUN bibechana-46416 7 6 energy energy NOUN bibechana-46416 7 7 , , PUNCT bibechana-46416 7 8 vibrational vibrational NOUN bibechana-46416 7 9 mean mean VERB bibechana-46416 7 10 free free ADJ bibechana-46416 7 11 energy energy NOUN bibechana-46416 7 12 , , PUNCT bibechana-46416 7 13 vibrational vibrational ADJ bibechana-46416 7 14 specific specific ADJ bibechana-46416 7 15 heat heat NOUN bibechana-46416 7 16 capacity capacity NOUN bibechana-46416 7 17 , , PUNCT bibechana-46416 7 18 and and CCONJ bibechana-46416 7 19 vibrational vibrational ADJ bibechana-46416 7 20 entropy entropy NOUN bibechana-46416 7 21 are be AUX bibechana-46416 7 22 obtained obtain VERB bibechana-46416 7 23 but but CCONJ bibechana-46416 7 24 due due ADP bibechana-46416 7 25 to to ADP bibechana-46416 7 26 complexity complexity NOUN bibechana-46416 7 27 , , PUNCT bibechana-46416 7 28 the the DET bibechana-46416 7 29 further further ADJ bibechana-46416 7 30 development development NOUN bibechana-46416 7 31 of of ADP bibechana-46416 7 32 the the DET bibechana-46416 7 33 equation equation NOUN bibechana-46416 7 34 is be AUX bibechana-46416 7 35 the the DET bibechana-46416 7 36 limitation limitation NOUN bibechana-46416 7 37 of of ADP bibechana-46416 7 38 this this DET bibechana-46416 7 39 work work NOUN bibechana-46416 7 40 . . PUNCT bibechana-46416 8 1 doi doi NOUN bibechana-46416 8 2 : : PUNCT bibechana-46416 8 3 https://doi.org/10.3126/bibechana.v19i1-2.46416 https://doi.org/10.3126/bibechana.v19i1-2.46416 NOUN bibechana-46416 8 4 this this DET bibechana-46416 8 5 work work NOUN bibechana-46416 8 6 is be AUX bibechana-46416 8 7 licensed license VERB bibechana-46416 8 8 under under ADP bibechana-46416 8 9 the the DET bibechana-46416 8 10 creative creative ADJ bibechana-46416 8 11 commons common NOUN bibechana-46416 8 12 cc cc ADP bibechana-46416 8 13 by by ADP bibechana-46416 8 14 - - PUNCT bibechana-46416 8 15 nc nc NOUN bibechana-46416 8 16 license license NOUN bibechana-46416 8 17 . . PUNCT bibechana-46416 9 1 https://creativecommons.org/ https://creativecommons.org/ PRON bibechana-46416 9 2 licenses license NOUN bibechana-46416 9 3 / / SYM bibechana-46416 9 4 by by ADP bibechana-46416 9 5 - - PUNCT bibechana-46416 9 6 nc/4.0/ nc/4.0/ NOUN bibechana-46416 9 7 bibechana bibechana NOUN bibechana-46416 9 8 issn issn VERB bibechana-46416 9 9 2091 2091 NUM bibechana-46416 9 10 - - SYM bibechana-46416 9 11 0762 0762 NUM bibechana-46416 9 12 ( ( PUNCT bibechana-46416 9 13 print print NOUN bibechana-46416 9 14 ) ) PUNCT bibechana-46416 9 15 , , PUNCT bibechana-46416 9 16 2382 2382 NUM bibechana-46416 9 17 - - SYM bibechana-46416 9 18 5340 5340 NUM bibechana-46416 9 19 ( ( PUNCT bibechana-46416 9 20 online online ADJ bibechana-46416 9 21 ) ) PUNCT bibechana-46416 9 22 journal journal NOUN bibechana-46416 9 23 homepage homepage NOUN bibechana-46416 9 24 : : PUNCT bibechana-46416 9 25 http://nepjol.info/index.php/bibechana http://nepjol.info/index.php/bibechana PROPN bibechana-46416 9 26 publisher publisher NOUN bibechana-46416 9 27 : : PUNCT bibechana-46416 9 28 department department NOUN bibechana-46416 9 29 of of ADP bibechana-46416 9 30 physics physics PROPN bibechana-46416 9 31 , , PUNCT bibechana-46416 9 32 mahendra mahendra PROPN bibechana-46416 9 33 morang morang PROPN bibechana-46416 9 34 a.m. a.m. PROPN bibechana-46416 10 1 campus campus PROPN bibechana-46416 10 2 , , PUNCT bibechana-46416 10 3 tu tu PROPN bibechana-46416 10 4 , , PUNCT bibechana-46416 10 5 biratnagar biratnagar NOUN bibechana-46416 10 6 , , PUNCT bibechana-46416 10 7 nepal nepal ADJ bibechana-46416 10 8 mailto:magnum.photon@gmail.com mailto:magnum.photon@gmail.com X bibechana-46416 11 1 https://doi.org/10.3126/bibechana.v19i1-2.46416 https://doi.org/10.3126/bibechana.v19i1-2.46416 X bibechana-46416 11 2 https://creativecommons.org/%20licenses/by-nc/4.0/ https://creativecommons.org/%20licenses/by-nc/4.0/ PROPN bibechana-46416 11 3 karki karki NOUN bibechana-46416 11 4 et et PROPN bibechana-46416 11 5 al al PROPN bibechana-46416 11 6 . . PUNCT bibechana-46416 11 7 / / SYM bibechana-46416 11 8 bibechana bibechana PROPN bibechana-46416 11 9 19(1 19(1 NUM bibechana-46416 11 10 - - SYM bibechana-46416 11 11 2 2 NUM bibechana-46416 11 12 ) ) PUNCT bibechana-46416 11 13 ( ( PUNCT bibechana-46416 11 14 2022 2022 NUM bibechana-46416 11 15 ) ) PUNCT bibechana-46416 11 16 165 165 NUM bibechana-46416 11 17 - - SYM bibechana-46416 11 18 169 169 NUM bibechana-46416 11 19 166 166 NUM bibechana-46416 11 20 1 1 NUM bibechana-46416 11 21 . . PUNCT bibechana-46416 12 1 introduction introduction NOUN bibechana-46416 12 2 deformation deformation NOUN bibechana-46416 12 3 hulthen hulthen NOUN bibechana-46416 12 4 potential potential NOUN bibechana-46416 12 5 ( ( PUNCT bibechana-46416 12 6 hp hp PROPN bibechana-46416 12 7 ) ) PUNCT bibechana-46416 12 8 with with ADP bibechana-46416 12 9 q q NOUN bibechana-46416 12 10 - - PUNCT bibechana-46416 12 11 deformation deformation NOUN bibechana-46416 12 12 is be AUX bibechana-46416 12 13 well well ADV bibechana-46416 12 14 - - PUNCT bibechana-46416 12 15 defined define VERB bibechana-46416 12 16 as as ADP bibechana-46416 12 17 𝑉(π‘Ÿ 𝑉(π‘Ÿ ADV bibechana-46416 12 18 ) ) PUNCT bibechana-46416 12 19 = = SYM bibechana-46416 13 1 βˆ’ βˆ’ PROPN bibechana-46416 13 2 𝑉0𝑒 𝑉0𝑒 PROPN bibechana-46416 13 3 βˆ’2π›Όπ‘Ÿ βˆ’2π›Όπ‘Ÿ VERB bibechana-46416 13 4 1 1 NUM bibechana-46416 13 5 βˆ’ βˆ’ NOUN bibechana-46416 13 6 π‘’βˆ’2π›Όπ‘Ÿ π‘’βˆ’2π›Όπ‘Ÿ ADV bibechana-46416 13 7 here here ADV bibechana-46416 13 8 𝑉0 𝑉0 X bibechana-46416 14 1 = = PUNCT bibechana-46416 15 1 𝑍𝑒 𝑍𝑒 PROPN bibechana-46416 15 2 2𝛼 2𝛼 PROPN bibechana-46416 15 3 is be AUX bibechana-46416 15 4 known know VERB bibechana-46416 15 5 as as ADP bibechana-46416 15 6 coupling couple VERB bibechana-46416 15 7 strength strength NOUN bibechana-46416 15 8 , , PUNCT bibechana-46416 15 9 and and CCONJ bibechana-46416 15 10 𝛼 𝛼 X bibechana-46416 15 11 is be AUX bibechana-46416 15 12 the the DET bibechana-46416 15 13 screening screening NOUN bibechana-46416 15 14 parameter parameter NOUN bibechana-46416 16 1 [ [ X bibechana-46416 16 2 1 1 NUM bibechana-46416 16 3 - - SYM bibechana-46416 16 4 5 5 NUM bibechana-46416 16 5 ] ] PUNCT bibechana-46416 16 6 . . PUNCT bibechana-46416 17 1 hp hp PROPN bibechana-46416 17 2 has have AUX bibechana-46416 17 3 introduced introduce VERB bibechana-46416 17 4 to to ADP bibechana-46416 17 5 studies study NOUN bibechana-46416 17 6 the the DET bibechana-46416 17 7 detail detail NOUN bibechana-46416 17 8 of of ADP bibechana-46416 17 9 deuteron deuteron NOUN bibechana-46416 17 10 and and CCONJ bibechana-46416 17 11 has have VERB bibechana-46416 17 12 extensive extensive ADJ bibechana-46416 17 13 applications application NOUN bibechana-46416 17 14 in in ADP bibechana-46416 17 15 physics physics NOUN bibechana-46416 17 16 like like ADP bibechana-46416 17 17 nuclear nuclear ADJ bibechana-46416 17 18 physics physics NOUN bibechana-46416 17 19 , , PUNCT bibechana-46416 17 20 particle particle NOUN bibechana-46416 17 21 physics physics PROPN bibechana-46416 17 22 , , PUNCT bibechana-46416 17 23 atomic atomic ADJ bibechana-46416 17 24 physics physics NOUN bibechana-46416 17 25 , , PUNCT bibechana-46416 17 26 condensed condense VERB bibechana-46416 17 27 matter matter NOUN bibechana-46416 17 28 physics physics NOUN bibechana-46416 17 29 , , PUNCT bibechana-46416 17 30 etc etc X bibechana-46416 17 31 . . X bibechana-46416 17 32 ) ) PUNCT bibechana-46416 17 33 . . PUNCT bibechana-46416 18 1 hp hp PROPN bibechana-46416 18 2 is be AUX bibechana-46416 18 3 one one NUM bibechana-46416 18 4 of of ADP bibechana-46416 18 5 the the DET bibechana-46416 18 6 short short ADJ bibechana-46416 18 7 - - PUNCT bibechana-46416 18 8 range range NOUN bibechana-46416 18 9 potentials potential NOUN bibechana-46416 18 10 like like ADP bibechana-46416 18 11 yukawa yukawa PROPN bibechana-46416 18 12 potential potential NOUN bibechana-46416 18 13 , , PUNCT bibechana-46416 18 14 which which PRON bibechana-46416 18 15 behaves behave VERB bibechana-46416 18 16 as as ADP bibechana-46416 18 17 a a DET bibechana-46416 18 18 coulomb coulomb NOUN bibechana-46416 18 19 potential potential NOUN bibechana-46416 18 20 at at ADP bibechana-46416 18 21 a a DET bibechana-46416 18 22 small small ADJ bibechana-46416 18 23 distance distance NOUN bibechana-46416 18 24 and and CCONJ bibechana-46416 18 25 exponentially exponentially ADV bibechana-46416 18 26 decreases decrease VERB bibechana-46416 18 27 with with ADP bibechana-46416 18 28 increasing increase VERB bibechana-46416 18 29 the the DET bibechana-46416 18 30 distance distance NOUN bibechana-46416 18 31 from from ADP bibechana-46416 18 32 the the DET bibechana-46416 18 33 nucleus nucleus NOUN bibechana-46416 18 34 . . PUNCT bibechana-46416 19 1 for for ADP bibechana-46416 19 2 spin spin NOUN bibechana-46416 19 3 - - PUNCT bibechana-46416 19 4 zero zero NUM bibechana-46416 19 5 particles particle NOUN bibechana-46416 19 6 , , PUNCT bibechana-46416 19 7 klein klein PROPN bibechana-46416 19 8 - - PUNCT bibechana-46416 19 9 gordon gordon PROPN bibechana-46416 19 10 uses use VERB bibechana-46416 19 11 hp hp PROPN bibechana-46416 19 12 for for ADP bibechana-46416 19 13 their their PRON bibechana-46416 19 14 equation equation NOUN bibechana-46416 19 15 to to PART bibechana-46416 19 16 solve solve VERB bibechana-46416 19 17 as as ADP bibechana-46416 19 18 𝑉(π‘Ÿ 𝑉(π‘Ÿ ADV bibechana-46416 19 19 ) ) PUNCT bibechana-46416 19 20 = = SYM bibechana-46416 19 21 βˆ’π‘π›Ό βˆ’π‘π›Ό NOUN bibechana-46416 19 22 exp(βˆ’ exp(βˆ’ PROPN bibechana-46416 19 23 π‘Ÿ π‘Ÿ NOUN bibechana-46416 19 24 π‘Ž π‘Ž X bibechana-46416 19 25 ) ) PUNCT bibechana-46416 19 26 1βˆ’exp(βˆ’ 1βˆ’exp(βˆ’ NUM bibechana-46416 19 27 π‘Ÿ π‘Ÿ NOUN bibechana-46416 19 28 π‘Ž π‘Ž X bibechana-46416 19 29 ) ) PUNCT bibechana-46416 19 30 or or CCONJ bibechana-46416 19 31 𝑉(π‘Ÿ 𝑉(π‘Ÿ NUM bibechana-46416 19 32 ) ) PUNCT bibechana-46416 19 33 = = SYM bibechana-46416 19 34 βˆ’π‘ βˆ’π‘ PROPN bibechana-46416 19 35 𝑒2𝛿 𝑒2𝛿 PROPN bibechana-46416 19 36 π‘’βˆ’π›Ώπ‘Ÿ π‘’βˆ’π›Ώπ‘Ÿ PROPN bibechana-46416 20 1 1βˆ’π‘’βˆ’π›Ώπ‘Ÿ 1βˆ’π‘’βˆ’π›Ώπ‘Ÿ NUM bibechana-46416 20 2 different different ADJ bibechana-46416 20 3 methods method NOUN bibechana-46416 20 4 like like ADP bibechana-46416 20 5 the the DET bibechana-46416 20 6 asymptotic asymptotic ADJ bibechana-46416 20 7 iteration iteration NOUN bibechana-46416 20 8 method method NOUN bibechana-46416 20 9 , , PUNCT bibechana-46416 20 10 supersymmetry supersymmetry NOUN bibechana-46416 20 11 method method NOUN bibechana-46416 20 12 , , PUNCT bibechana-46416 20 13 shift shift VERB bibechana-46416 20 14 n1 n1 ADJ bibechana-46416 20 15 expression expression NOUN bibechana-46416 20 16 , , PUNCT bibechana-46416 20 17 factorization factorization NOUN bibechana-46416 20 18 method method NOUN bibechana-46416 20 19 , , PUNCT bibechana-46416 20 20 nikiforov nikiforov NOUN bibechana-46416 20 21 - - PUNCT bibechana-46416 20 22 uvarove uvarove ADJ bibechana-46416 20 23 , , PUNCT bibechana-46416 20 24 etc etc X bibechana-46416 20 25 . . X bibechana-46416 20 26 , , PUNCT bibechana-46416 20 27 are be AUX bibechana-46416 20 28 used use VERB bibechana-46416 20 29 to to PART bibechana-46416 20 30 calculate calculate VERB bibechana-46416 20 31 energy energy NOUN bibechana-46416 20 32 eigenvalue eigenvalue NOUN bibechana-46416 20 33 for for ADP bibechana-46416 20 34 further further ADJ bibechana-46416 20 35 potential potential NOUN bibechana-46416 20 36 . . PUNCT bibechana-46416 21 1 the the DET bibechana-46416 21 2 q q ADV bibechana-46416 21 3 - - PUNCT bibechana-46416 21 4 deformed deform VERB bibechana-46416 21 5 hp hp NOUN bibechana-46416 21 6 and and CCONJ bibechana-46416 21 7 modified modify VERB bibechana-46416 21 8 inversely inversely ADV bibechana-46416 21 9 quadratic quadratic ADJ bibechana-46416 21 10 yukawa yukawa PROPN bibechana-46416 21 11 ( ( PUNCT bibechana-46416 21 12 qdhmiqy qdhmiqy ADJ bibechana-46416 21 13 ) ) PUNCT bibechana-46416 21 14 potential potential NOUN bibechana-46416 21 15 can can AUX bibechana-46416 21 16 be be AUX bibechana-46416 21 17 represented represent VERB bibechana-46416 21 18 as as ADP bibechana-46416 21 19 , , PUNCT bibechana-46416 21 20 𝑉(π‘Ÿ 𝑉(π‘Ÿ NUM bibechana-46416 21 21 ) ) PUNCT bibechana-46416 21 22 = = SYM bibechana-46416 22 1 βˆ’ βˆ’ PROPN bibechana-46416 22 2 𝑉0𝑒 𝑉0𝑒 PROPN bibechana-46416 22 3 βˆ’2π›Όπ‘Ÿ βˆ’2π›Όπ‘Ÿ VERB bibechana-46416 22 4 1 1 NUM bibechana-46416 22 5 βˆ’ βˆ’ NOUN bibechana-46416 22 6 π‘žπ‘’βˆ’2π›Όπ‘Ÿ π‘žπ‘’βˆ’2π›Όπ‘Ÿ ADP bibechana-46416 22 7 βˆ’ βˆ’ PROPN bibechana-46416 22 8 𝑉1𝑒 𝑉1𝑒 NOUN bibechana-46416 22 9 βˆ’2π›Όπ‘Ÿ βˆ’2π›Όπ‘Ÿ ADJ bibechana-46416 22 10 π‘Ÿ2 π‘Ÿ2 NOUN bibechana-46416 22 11 here here ADV bibechana-46416 22 12 𝑉0 𝑉0 NOUN bibechana-46416 22 13 , , PUNCT bibechana-46416 22 14 𝑉1 𝑉1 PROPN bibechana-46416 22 15 , , PUNCT bibechana-46416 22 16 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN bibechana-46416 22 17 π‘ž π‘ž PROPN bibechana-46416 22 18 are be AUX bibechana-46416 22 19 coupling couple VERB bibechana-46416 22 20 strength strength NOUN bibechana-46416 22 21 and and CCONJ bibechana-46416 22 22 deformation deformation NOUN bibechana-46416 22 23 parameters parameter NOUN bibechana-46416 22 24 , , PUNCT bibechana-46416 22 25 respectively respectively ADV bibechana-46416 22 26 . . PUNCT bibechana-46416 23 1 such such ADJ bibechana-46416 23 2 potential potential NOUN bibechana-46416 23 3 is be AUX bibechana-46416 23 4 used use VERB bibechana-46416 23 5 to to PART bibechana-46416 23 6 describe describe VERB bibechana-46416 23 7 different different ADJ bibechana-46416 23 8 interactions interaction NOUN bibechana-46416 23 9 such such ADJ bibechana-46416 23 10 as as ADP bibechana-46416 23 11 nucleon nucleon NOUN bibechana-46416 23 12 - - PUNCT bibechana-46416 23 13 nucleon nucleon NOUN bibechana-46416 23 14 interactions interaction NOUN bibechana-46416 23 15 , , PUNCT bibechana-46416 23 16 meson meson NOUN bibechana-46416 23 17 - - PUNCT bibechana-46416 23 18 meson meson NOUN bibechana-46416 23 19 interactions interaction NOUN bibechana-46416 23 20 , , PUNCT bibechana-46416 23 21 the the DET bibechana-46416 23 22 various various ADJ bibechana-46416 23 23 field field NOUN bibechana-46416 23 24 of of ADP bibechana-46416 23 25 nuclear nuclear ADJ bibechana-46416 23 26 physics physic NOUN bibechana-46416 23 27 , , PUNCT bibechana-46416 23 28 and and CCONJ bibechana-46416 23 29 quantum quantum ADJ bibechana-46416 23 30 chemistry chemistry NOUN bibechana-46416 23 31 ( ( PUNCT bibechana-46416 23 32 hulthen hulthen ADV bibechana-46416 23 33 , , PUNCT bibechana-46416 23 34 1942 1942 NUM bibechana-46416 23 35 and and CCONJ bibechana-46416 23 36 tencan tencan PROPN bibechana-46416 23 37 & & CCONJ bibechana-46416 23 38 sever sever VERB bibechana-46416 23 39 , , PUNCT bibechana-46416 23 40 2009 2009 NUM bibechana-46416 23 41 ) ) PUNCT bibechana-46416 23 42 . . PUNCT bibechana-46416 24 1 1.1 1.1 NUM bibechana-46416 24 2 . . PUNCT bibechana-46416 25 1 differntent differntent ADJ bibechana-46416 25 2 method method NOUN bibechana-46416 25 3 to to PART bibechana-46416 25 4 calcaulte calcaulte NOUN bibechana-46416 25 5 energy energy NOUN bibechana-46416 25 6 eigenvalue eigenvalue PROPN bibechana-46416 25 7 1.1.1 1.1.1 NUM bibechana-46416 25 8 . . PUNCT bibechana-46416 26 1 asymptotic asymptotic ADJ bibechana-46416 26 2 iteration iteration NOUN bibechana-46416 26 3 method method NOUN bibechana-46416 26 4 this this DET bibechana-46416 26 5 method method NOUN bibechana-46416 26 6 is be AUX bibechana-46416 26 7 used use VERB bibechana-46416 26 8 to to PART bibechana-46416 26 9 solve solve VERB bibechana-46416 26 10 homogenous homogenous ADJ bibechana-46416 26 11 linear linear ADJ bibechana-46416 26 12 second second ADJ bibechana-46416 26 13 - - PUNCT bibechana-46416 26 14 order order NOUN bibechana-46416 26 15 differential differential ADJ bibechana-46416 26 16 equations equation NOUN bibechana-46416 26 17 defined define VERB bibechana-46416 26 18 as as ADP bibechana-46416 26 19 , , PUNCT bibechana-46416 26 20 𝑦 𝑦 NOUN bibechana-46416 26 21 " " PUNCT bibechana-46416 26 22 = = SYM bibechana-46416 26 23 πœ†0(π‘₯)𝑦′ πœ†0(π‘₯)𝑦′ PROPN bibechana-46416 26 24 + + CCONJ bibechana-46416 26 25 𝑠0(π‘₯)𝑦 𝑠0(π‘₯)𝑦 NUM bibechana-46416 26 26 , , PUNCT bibechana-46416 26 27 here here ADV bibechana-46416 26 28 πœ†0(π‘₯ πœ†0(π‘₯ ADP bibechana-46416 26 29 ) ) PUNCT bibechana-46416 26 30 and and CCONJ bibechana-46416 26 31 𝑠0(π‘₯ 𝑠0(π‘₯ PROPN bibechana-46416 26 32 ) ) PUNCT bibechana-46416 26 33 function function NOUN bibechana-46416 26 34 in in ADP bibechana-46416 26 35 𝐢∞(π‘Ž 𝐢∞(π‘Ž PROPN bibechana-46416 26 36 , , PUNCT bibechana-46416 26 37 𝑏 𝑏 NOUN bibechana-46416 26 38 ) ) PUNCT bibechana-46416 26 39 . . PUNCT bibechana-46416 27 1 on on ADP bibechana-46416 27 2 taking take VERB bibechana-46416 27 3 ( ( PUNCT bibechana-46416 27 4 n+1)th n+1)th NOUN bibechana-46416 27 5 and and CCONJ bibechana-46416 27 6 ( ( PUNCT bibechana-46416 27 7 n+2)the n+2)the PRON bibechana-46416 27 8 derivative derivative ADJ bibechana-46416 27 9 , , PUNCT bibechana-46416 27 10 we we PRON bibechana-46416 27 11 get get VERB bibechana-46416 27 12 , , PUNCT bibechana-46416 27 13 𝑦(𝑛+1 𝑦(𝑛+1 NOUN bibechana-46416 27 14 ) ) PUNCT bibechana-46416 27 15 = = PUNCT bibechana-46416 28 1 πœ†π‘›βˆ’1(π‘₯)𝑦′ πœ†π‘›βˆ’1(π‘₯)𝑦′ NOUN bibechana-46416 28 2 + + CCONJ bibechana-46416 28 3 π‘ π‘›βˆ’1(π‘₯)𝑦 π‘ π‘›βˆ’1(π‘₯)𝑦 ADP bibechana-46416 28 4 and and CCONJ bibechana-46416 28 5 𝑦(𝑛+2 𝑦(𝑛+2 NUM bibechana-46416 28 6 ) ) PUNCT bibechana-46416 29 1 = = NOUN bibechana-46416 29 2 πœ†π‘›(π‘₯)𝑦′ πœ†π‘›(π‘₯)𝑦′ PUNCT bibechana-46416 30 1 + + PUNCT bibechana-46416 30 2 𝑠𝑛(π‘₯)𝑦 𝑠𝑛(π‘₯)𝑦 PROPN bibechana-46416 30 3 . . PUNCT bibechana-46416 31 1 here here ADV bibechana-46416 31 2 πœ†π‘› πœ†π‘› ADP bibechana-46416 31 3 = = PUNCT bibechana-46416 31 4 πœ†π‘›βˆ’1 πœ†π‘›βˆ’1 NOUN bibechana-46416 31 5 β€² β€² NOUN bibechana-46416 32 1 + + CCONJ bibechana-46416 32 2 π‘ π‘›βˆ’1 π‘ π‘›βˆ’1 PROPN bibechana-46416 32 3 + + CCONJ bibechana-46416 32 4 πœ†0πœ†π‘›βˆ’1 πœ†0πœ†π‘›βˆ’1 NUM bibechana-46416 32 5 and and CCONJ bibechana-46416 32 6 𝑠𝑛 𝑠𝑛 NOUN bibechana-46416 32 7 = = SYM bibechana-46416 32 8 π‘ π‘›βˆ’1 π‘ π‘›βˆ’1 NOUN bibechana-46416 32 9 β€² β€² NOUN bibechana-46416 32 10 + + CCONJ bibechana-46416 32 11 𝑠0πœ†π‘›βˆ’1 𝑠0πœ†π‘›βˆ’1 NUM bibechana-46416 32 12 . . PUNCT bibechana-46416 33 1 on on ADP bibechana-46416 33 2 taking take VERB bibechana-46416 33 3 the the DET bibechana-46416 33 4 ratio ratio NOUN bibechana-46416 33 5 of of ADP bibechana-46416 33 6 ( ( PUNCT bibechana-46416 33 7 n+2)th n+2)th PROPN bibechana-46416 33 8 and and CCONJ bibechana-46416 33 9 ( ( PUNCT bibechana-46416 33 10 n+1)th n+1)th PROPN bibechana-46416 33 11 and and CCONJ bibechana-46416 33 12 applying apply VERB bibechana-46416 33 13 the the DET bibechana-46416 33 14 asymptotic asymptotic ADJ bibechana-46416 33 15 condition condition NOUN bibechana-46416 33 16 𝑠𝑛 𝑠𝑛 NOUN bibechana-46416 33 17 πœ†π‘› πœ†π‘› NOUN bibechana-46416 34 1 = = SYM bibechana-46416 34 2 π‘ π‘›βˆ’1 π‘ π‘›βˆ’1 PROPN bibechana-46416 34 3 πœ†π‘›βˆ’1 πœ†π‘›βˆ’1 PROPN bibechana-46416 34 4 ≔ ≔ NOUN bibechana-46416 34 5 𝛼 𝛼 NOUN bibechana-46416 34 6 , , PUNCT bibechana-46416 34 7 the the DET bibechana-46416 34 8 condition condition NOUN bibechana-46416 34 9 gives give VERB bibechana-46416 34 10 the the DET bibechana-46416 34 11 eigenvalue eigenvalue NOUN bibechana-46416 34 12 of of ADP bibechana-46416 34 13 the the DET bibechana-46416 34 14 considered consider VERB bibechana-46416 34 15 equation equation NOUN bibechana-46416 34 16 , , PUNCT bibechana-46416 34 17 and and CCONJ bibechana-46416 34 18 we we PRON bibechana-46416 34 19 obtained obtain VERB bibechana-46416 34 20 𝑦(𝑛+1)(π‘₯ 𝑦(𝑛+1)(π‘₯ NOUN bibechana-46416 34 21 ) ) PUNCT bibechana-46416 34 22 = = SYM bibechana-46416 34 23 𝐢1πœ†π‘›βˆ’1 𝐢1πœ†π‘›βˆ’1 NOUN bibechana-46416 34 24 exp exp NOUN bibechana-46416 34 25 ( ( PUNCT bibechana-46416 34 26 ∫ ∫ PROPN bibechana-46416 34 27 ( ( PUNCT bibechana-46416 34 28 𝛼 𝛼 NOUN bibechana-46416 34 29 + + NUM bibechana-46416 34 30 πœ†0)𝑑𝑑 πœ†0)𝑑𝑑 PROPN bibechana-46416 34 31 π‘₯ π‘₯ NOUN bibechana-46416 34 32 ) ) PUNCT bibechana-46416 34 33 this this DET bibechana-46416 34 34 equation equation NOUN bibechana-46416 34 35 yields yield VERB bibechana-46416 34 36 the the DET bibechana-46416 34 37 solution solution NOUN bibechana-46416 34 38 of of ADP bibechana-46416 34 39 the the DET bibechana-46416 34 40 asymptotic asymptotic ADJ bibechana-46416 34 41 consider consider VERB bibechana-46416 34 42 equation equation NOUN bibechana-46416 34 43 as as ADP bibechana-46416 34 44 𝑦(π‘₯ 𝑦(π‘₯ NOUN bibechana-46416 34 45 ) ) PUNCT bibechana-46416 34 46 = = PUNCT bibechana-46416 35 1 [ [ X bibechana-46416 35 2 𝐢2 𝐢2 X bibechana-46416 35 3 + + NUM bibechana-46416 35 4 𝐢1∫ 𝐢1∫ ADJ bibechana-46416 35 5 exp exp NOUN bibechana-46416 35 6 ( ( PUNCT bibechana-46416 35 7 ∫ ∫ PROPN bibechana-46416 35 8 ( ( PUNCT bibechana-46416 35 9 πœ†0(𝜏 πœ†0(𝜏 PROPN bibechana-46416 35 10 ) ) PUNCT bibechana-46416 35 11 + + NUM bibechana-46416 35 12 2𝛼(𝜏))π‘‘πœ 2𝛼(𝜏))π‘‘πœ NUM bibechana-46416 35 13 𝑑 𝑑 NOUN bibechana-46416 35 14 ) ) PUNCT bibechana-46416 35 15 𝑑𝑑 𝑑𝑑 ADP bibechana-46416 35 16 π‘₯ π‘₯ NOUN bibechana-46416 35 17 ] ] X bibechana-46416 35 18 1.1.2 1.1.2 X bibechana-46416 35 19 . . PUNCT bibechana-46416 36 1 nikiforov nikiforov NOUN bibechana-46416 36 2 - - PUNCT bibechana-46416 36 3 uvarov uvarov PROPN bibechana-46416 36 4 this this DET bibechana-46416 36 5 method method NOUN bibechana-46416 36 6 is be AUX bibechana-46416 36 7 used use VERB bibechana-46416 36 8 to to PART bibechana-46416 36 9 solve solve VERB bibechana-46416 36 10 the the DET bibechana-46416 36 11 solution solution NOUN bibechana-46416 36 12 of of ADP bibechana-46416 36 13 an an DET bibechana-46416 36 14 equation equation NOUN bibechana-46416 36 15 ( ( PUNCT bibechana-46416 36 16 e.g. e.g. ADV bibechana-46416 36 17 , , PUNCT bibechana-46416 36 18 schrodinger schrodinger NOUN bibechana-46416 36 19 ) ) PUNCT bibechana-46416 36 20 by by ADP bibechana-46416 36 21 transformation transformation NOUN bibechana-46416 36 22 as as ADP bibechana-46416 36 23 πœ“β€²β€²(𝑠 πœ“β€²β€²(𝑠 NOUN bibechana-46416 36 24 ) ) PUNCT bibechana-46416 37 1 + + CCONJ bibechana-46416 37 2 οΏ½ οΏ½ PROPN bibechana-46416 37 3 Μƒ Μƒ NOUN bibechana-46416 37 4 οΏ½ οΏ½ NOUN bibechana-46416 37 5 (𝑠 (𝑠 NOUN bibechana-46416 37 6 ) ) PUNCT bibechana-46416 37 7 𝜎(𝑠 𝜎(𝑠 PROPN bibechana-46416 37 8 ) ) PUNCT bibechana-46416 37 9 πœ“β€²(𝑠 πœ“β€²(𝑠 PROPN bibechana-46416 37 10 ) ) PUNCT bibechana-46416 37 11 + + CCONJ bibechana-46416 37 12 οΏ½ οΏ½ PROPN bibechana-46416 37 13 Μƒ Μƒ NOUN bibechana-46416 37 14 οΏ½ οΏ½ NOUN bibechana-46416 37 15 (𝑠 (𝑠 NOUN bibechana-46416 37 16 ) ) PUNCT bibechana-46416 37 17 𝜎2(𝑠 𝜎2(𝑠 PROPN bibechana-46416 37 18 ) ) PUNCT bibechana-46416 37 19 πœ“(𝑠 πœ“(𝑠 NOUN bibechana-46416 37 20 ) ) PUNCT bibechana-46416 38 1 = = PUNCT bibechana-46416 38 2 0 0 NUM bibechana-46416 38 3 , , PUNCT bibechana-46416 38 4 here here ADV bibechana-46416 38 5 οΏ½ οΏ½ PROPN bibechana-46416 38 6 Μƒ Μƒ NOUN bibechana-46416 38 7 οΏ½ οΏ½ NOUN bibechana-46416 38 8 (𝑠 (𝑠 NOUN bibechana-46416 38 9 ) ) PUNCT bibechana-46416 38 10 is be AUX bibechana-46416 38 11 polynomial polynomial ADJ bibechana-46416 38 12 of of ADP bibechana-46416 38 13 degree degree NOUN bibechana-46416 38 14 at at ADP bibechana-46416 38 15 most most ADV bibechana-46416 38 16 one one NUM bibechana-46416 38 17 , , PUNCT bibechana-46416 38 18 𝜎(𝑠 𝜎(𝑠 PROPN bibechana-46416 38 19 ) ) PUNCT bibechana-46416 38 20 and and CCONJ bibechana-46416 38 21 οΏ½ οΏ½ PROPN bibechana-46416 38 22 Μƒ Μƒ PROPN bibechana-46416 38 23 οΏ½ οΏ½ NOUN bibechana-46416 38 24 (𝑠 (𝑠 NOUN bibechana-46416 38 25 ) ) PUNCT bibechana-46416 38 26 are be AUX bibechana-46416 38 27 second second ADJ bibechana-46416 38 28 - - PUNCT bibechana-46416 38 29 degree degree NOUN bibechana-46416 38 30 polynomials polynomial NOUN bibechana-46416 38 31 . . PUNCT bibechana-46416 39 1 on on ADP bibechana-46416 39 2 applying apply VERB bibechana-46416 39 3 the the DET bibechana-46416 39 4 condition condition NOUN bibechana-46416 39 5 of of ADP bibechana-46416 39 6 πœ† πœ† NOUN bibechana-46416 39 7 = = SYM bibechana-46416 39 8 πœ†π‘› πœ†π‘› ADP bibechana-46416 39 9 one one NOUN bibechana-46416 39 10 can can AUX bibechana-46416 39 11 obtain obtain VERB bibechana-46416 39 12 the the DET bibechana-46416 39 13 energy energy NOUN bibechana-46416 39 14 eigenvalue eigenvalue NOUN bibechana-46416 39 15 . . PUNCT bibechana-46416 40 1 here here ADV bibechana-46416 40 2 πœ† πœ† PRON bibechana-46416 40 3 = = PUNCT bibechana-46416 40 4 π‘˜βˆ’ π‘˜βˆ’ X bibechana-46416 40 5 + + PUNCT bibechana-46416 40 6 πœ‹β€²(𝑠 πœ‹β€²(𝑠 CCONJ bibechana-46416 40 7 ) ) PUNCT bibechana-46416 40 8 and and CCONJ bibechana-46416 40 9 πœ†π‘› πœ†π‘› NOUN bibechana-46416 40 10 = = SYM bibechana-46416 40 11 βˆ’π‘›πœ βˆ’π‘›πœ PROPN bibechana-46416 40 12 β€²(𝑠 β€²(𝑠 NOUN bibechana-46416 40 13 ) ) PUNCT bibechana-46416 41 1 βˆ’ βˆ’ PROPN bibechana-46416 41 2 𝑛(π‘›βˆ’1)πœŽβ€²β€²(𝑠 𝑛(π‘›βˆ’1)πœŽβ€²β€²(𝑠 NOUN bibechana-46416 41 3 ) ) PUNCT bibechana-46416 41 4 2 2 NUM bibechana-46416 41 5 , , PUNCT bibechana-46416 41 6 πœ‹(𝑠 πœ‹(𝑠 NOUN bibechana-46416 41 7 ) ) PUNCT bibechana-46416 41 8 is be AUX bibechana-46416 41 9 also also ADV bibechana-46416 41 10 polynomial polynomial ADJ bibechana-46416 41 11 with with ADP bibechana-46416 41 12 four four NUM bibechana-46416 41 13 values value NOUN bibechana-46416 41 14 obtained obtain VERB bibechana-46416 41 15 by by ADP bibechana-46416 41 16 comparing compare VERB bibechana-46416 41 17 the the DET bibechana-46416 41 18 standard standard ADJ bibechana-46416 41 19 equation equation NOUN bibechana-46416 41 20 . . PUNCT bibechana-46416 42 1 1.1.3 1.1.3 X bibechana-46416 42 2 . . PUNCT bibechana-46416 43 1 supersymmetry supersymmetry NOUN bibechana-46416 43 2 method method NOUN bibechana-46416 43 3 to to PART bibechana-46416 43 4 calculate calculate VERB bibechana-46416 43 5 the the DET bibechana-46416 43 6 energy energy NOUN bibechana-46416 43 7 eigenvalue eigenvalue NOUN bibechana-46416 43 8 , , PUNCT bibechana-46416 43 9 this this DET bibechana-46416 43 10 method method NOUN bibechana-46416 43 11 assumes assume VERB bibechana-46416 43 12 a a DET bibechana-46416 43 13 particular particular ADJ bibechana-46416 43 14 type type NOUN bibechana-46416 43 15 of of ADP bibechana-46416 43 16 wave wave NOUN bibechana-46416 43 17 function function NOUN bibechana-46416 43 18 πœ“π‘  πœ“π‘  ADP bibechana-46416 43 19 = = PUNCT bibechana-46416 43 20 exp[βˆ«π‘Š0(π‘Ÿ)π‘‘π‘Ÿ exp[βˆ«π‘Š0(π‘Ÿ)π‘‘π‘Ÿ PROPN bibechana-46416 43 21 + + CCONJ bibechana-46416 43 22 𝛽(π‘Ÿ)]πœ™π‘ (π‘Ÿ 𝛽(π‘Ÿ)]πœ™π‘ (π‘Ÿ NOUN bibechana-46416 43 23 ) ) PUNCT bibechana-46416 43 24 , , PUNCT bibechana-46416 43 25 here here ADV bibechana-46416 43 26 π‘Š0(π‘Ÿ π‘Š0(π‘Ÿ PROPN bibechana-46416 43 27 ) ) PUNCT bibechana-46416 43 28 is be AUX bibechana-46416 43 29 supersymmetry supersymmetry NOUN bibechana-46416 43 30 in in ADP bibechana-46416 43 31 quantum quantum ADJ bibechana-46416 43 32 mechanics mechanic NOUN bibechana-46416 43 33 assumed assume VERB bibechana-46416 43 34 as as ADP bibechana-46416 43 35 witten witten PROPN bibechana-46416 43 36 superpotential superpotential NOUN bibechana-46416 43 37 , , PUNCT bibechana-46416 43 38 πœ™π‘ (π‘Ÿ πœ™π‘ (π‘Ÿ NUM bibechana-46416 43 39 ) ) PUNCT bibechana-46416 43 40 is be AUX bibechana-46416 43 41 a a DET bibechana-46416 43 42 new new ADJ bibechana-46416 43 43 function function NOUN bibechana-46416 43 44 , , PUNCT bibechana-46416 43 45 and and CCONJ bibechana-46416 43 46 𝛽(π‘Ÿ 𝛽(π‘Ÿ NOUN bibechana-46416 43 47 ) ) PUNCT bibechana-46416 43 48 is be AUX bibechana-46416 43 49 also also ADV bibechana-46416 43 50 a a DET bibechana-46416 43 51 wave wave NOUN bibechana-46416 43 52 function function NOUN bibechana-46416 43 53 that that PRON bibechana-46416 43 54 leads lead VERB bibechana-46416 43 55 to to PART bibechana-46416 43 56 correct correct VERB bibechana-46416 43 57 asymptotic asymptotic ADJ bibechana-46416 43 58 value value NOUN bibechana-46416 43 59 . . PUNCT bibechana-46416 44 1 as as SCONJ bibechana-46416 44 2 we we PRON bibechana-46416 44 3 knew know VERB bibechana-46416 44 4 schrodinger schrodinger ADJ bibechana-46416 44 5 equation equation NOUN bibechana-46416 44 6 is be AUX bibechana-46416 44 7 used use VERB bibechana-46416 44 8 to to PART bibechana-46416 44 9 obtain obtain VERB bibechana-46416 44 10 the the DET bibechana-46416 44 11 energy energy NOUN bibechana-46416 44 12 eigenvalue eigenvalue NOUN bibechana-46416 44 13 by by ADP bibechana-46416 44 14 replacing replace VERB bibechana-46416 44 15 the the DET bibechana-46416 44 16 general general ADJ bibechana-46416 44 17 wave wave NOUN bibechana-46416 44 18 function function NOUN bibechana-46416 44 19 by by ADP bibechana-46416 44 20 πœ“π‘  πœ“π‘  ADV bibechana-46416 44 21 and and CCONJ bibechana-46416 44 22 solving solve VERB bibechana-46416 44 23 similar similar ADJ bibechana-46416 44 24 to to ADP bibechana-46416 44 25 the the DET bibechana-46416 44 26 conventional conventional ADJ bibechana-46416 44 27 method method NOUN bibechana-46416 44 28 , , PUNCT bibechana-46416 44 29 we we PRON bibechana-46416 44 30 get get VERB bibechana-46416 44 31 energy energy NOUN bibechana-46416 44 32 eigenvalue eigenvalue NOUN bibechana-46416 44 33 for for ADP bibechana-46416 44 34 any any DET bibechana-46416 44 35 potential potential NOUN bibechana-46416 44 36 . . PUNCT bibechana-46416 45 1 1.1.4 1.1.4 NUM bibechana-46416 45 2 . . PUNCT bibechana-46416 45 3 factorization factorization NOUN bibechana-46416 45 4 method method NOUN bibechana-46416 45 5 in in ADP bibechana-46416 45 6 this this DET bibechana-46416 45 7 method method NOUN bibechana-46416 45 8 , , PUNCT bibechana-46416 45 9 the the DET bibechana-46416 45 10 wave wave NOUN bibechana-46416 45 11 function function NOUN bibechana-46416 45 12 for for ADP bibechana-46416 45 13 a a DET bibechana-46416 45 14 particular particular ADJ bibechana-46416 45 15 coordinate coordinate NOUN bibechana-46416 45 16 system system NOUN bibechana-46416 45 17 ( ( PUNCT bibechana-46416 45 18 example example NOUN bibechana-46416 45 19 , , PUNCT bibechana-46416 45 20 schrodinger schrodinger ADJ bibechana-46416 45 21 equation equation NOUN bibechana-46416 45 22 spherical spherical ADJ bibechana-46416 45 23 coordinate coordinate NOUN bibechana-46416 45 24 system system NOUN bibechana-46416 45 25 ) ) PUNCT bibechana-46416 45 26 contains contain VERB bibechana-46416 45 27 angular angular ADJ bibechana-46416 45 28 and and CCONJ bibechana-46416 45 29 coordinate coordinate NOUN bibechana-46416 45 30 system system NOUN bibechana-46416 45 31 , , PUNCT bibechana-46416 45 32 and and CCONJ bibechana-46416 45 33 this this DET bibechana-46416 45 34 method method NOUN bibechana-46416 45 35 separates separate VERB bibechana-46416 45 36 the the DET bibechana-46416 45 37 angular angular ADJ bibechana-46416 45 38 and and CCONJ bibechana-46416 45 39 radial radial ADJ bibechana-46416 45 40 part part NOUN bibechana-46416 45 41 by by ADP bibechana-46416 45 42 factorization factorization NOUN bibechana-46416 45 43 method method NOUN bibechana-46416 45 44 known know VERB bibechana-46416 45 45 as as ADP bibechana-46416 45 46 separation separation NOUN bibechana-46416 45 47 of of ADP bibechana-46416 45 48 variable variable NOUN bibechana-46416 45 49 in in ADP bibechana-46416 45 50 general general ADJ bibechana-46416 45 51 like like ADP bibechana-46416 45 52 ψ(π‘Ÿ ψ(π‘Ÿ NOUN bibechana-46416 45 53 , , PUNCT bibechana-46416 45 54 πœƒ πœƒ NOUN bibechana-46416 45 55 , , PUNCT bibechana-46416 45 56 πœ™ πœ™ NOUN bibechana-46416 45 57 ) ) PUNCT bibechana-46416 45 58 = = SYM bibechana-46416 45 59 𝑅(π‘Ÿ)ΞΈ(πœƒ)Ο†(πœ™ 𝑅(π‘Ÿ)ΞΈ(πœƒ)Ο†(πœ™ NOUN bibechana-46416 45 60 ) ) PUNCT bibechana-46416 45 61 after after ADP bibechana-46416 45 62 separating separate VERB bibechana-46416 45 63 the the DET bibechana-46416 45 64 angular angular ADJ bibechana-46416 45 65 and and CCONJ bibechana-46416 45 66 radial radial ADJ bibechana-46416 45 67 parts part NOUN bibechana-46416 45 68 . . PUNCT bibechana-46416 46 1 the the DET bibechana-46416 46 2 radial radial ADJ bibechana-46416 46 3 part part NOUN bibechana-46416 46 4 is be AUX bibechana-46416 46 5 defined define VERB bibechana-46416 46 6 as as ADP bibechana-46416 46 7 𝑅(π‘Ÿ 𝑅(π‘Ÿ NOUN bibechana-46416 46 8 ) ) PUNCT bibechana-46416 46 9 = = SYM bibechana-46416 47 1 π‘ˆ(π‘Ÿ)𝐿(π‘Ÿ π‘ˆ(π‘Ÿ)𝐿(π‘Ÿ NOUN bibechana-46416 47 2 ) ) PUNCT bibechana-46416 47 3 , , PUNCT bibechana-46416 47 4 here here ADV bibechana-46416 47 5 u(r u(r ADV bibechana-46416 47 6 ) ) PUNCT bibechana-46416 47 7 is be AUX bibechana-46416 47 8 related relate VERB bibechana-46416 47 9 to to ADP bibechana-46416 47 10 potential potential ADJ bibechana-46416 47 11 and and CCONJ bibechana-46416 47 12 l(r l(r PROPN bibechana-46416 47 13 ) ) PUNCT bibechana-46416 47 14 is be AUX bibechana-46416 47 15 associated associate VERB bibechana-46416 47 16 with with ADP bibechana-46416 47 17 laguerre laguerre NOUN bibechana-46416 47 18 differential differential NOUN bibechana-46416 47 19 equation equation NOUN bibechana-46416 47 20 . . PUNCT bibechana-46416 48 1 the the DET bibechana-46416 48 2 angular angular ADJ bibechana-46416 48 3 part part NOUN bibechana-46416 48 4 is be AUX bibechana-46416 48 5 defined define VERB bibechana-46416 48 6 as as ADP bibechana-46416 48 7 ΞΈ(π‘₯ ΞΈ(π‘₯ NOUN bibechana-46416 48 8 ) ) PUNCT bibechana-46416 48 9 = = SYM bibechana-46416 49 1 π‘ˆ(π‘₯)𝑃(π‘₯ π‘ˆ(π‘₯)𝑃(π‘₯ NOUN bibechana-46416 49 2 ) ) PUNCT bibechana-46416 49 3 , , PUNCT bibechana-46416 49 4 here here ADV bibechana-46416 49 5 π‘₯ π‘₯ PROPN bibechana-46416 49 6 = = PUNCT bibechana-46416 49 7 π‘π‘œπ‘ πœƒ π‘π‘œπ‘ πœƒ NOUN bibechana-46416 49 8 , , PUNCT bibechana-46416 49 9 p(x p(x PROPN bibechana-46416 49 10 ) ) PUNCT bibechana-46416 49 11 related relate VERB bibechana-46416 49 12 to to ADP bibechana-46416 49 13 the the DET bibechana-46416 49 14 jacobi jacobi PROPN bibechana-46416 49 15 function function NOUN bibechana-46416 49 16 . . PUNCT bibechana-46416 50 1 2 2 X bibechana-46416 50 2 . . X bibechana-46416 50 3 theoretical theoretical ADJ bibechana-46416 50 4 formulation formulation NOUN bibechana-46416 50 5 we we PRON bibechana-46416 50 6 have have VERB bibechana-46416 50 7 radial radial ADJ bibechana-46416 50 8 form form NOUN bibechana-46416 50 9 part part NOUN bibechana-46416 50 10 of of ADP bibechana-46416 50 11 se se PROPN bibechana-46416 50 12 is be AUX bibechana-46416 50 13 πœ“β€²β€²(π‘Ÿ πœ“β€²β€²(π‘Ÿ NOUN bibechana-46416 50 14 ) ) PUNCT bibechana-46416 51 1 + + NUM bibechana-46416 51 2 2π‘š 2π‘š NUM bibechana-46416 51 3 ℏ2 ℏ2 NOUN bibechana-46416 51 4 [ [ X bibechana-46416 51 5 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 51 6 βˆ’ βˆ’ PROPN bibechana-46416 51 7 𝑉(π‘Ÿ 𝑉(π‘Ÿ ADV bibechana-46416 51 8 ) ) PUNCT bibechana-46416 51 9 βˆ’ βˆ’ PROPN bibechana-46416 52 1 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 53 1 + + NUM bibechana-46416 53 2 1)ℏ 1)ℏ NOUN bibechana-46416 53 3 2π‘šπ‘Ÿ2 2π‘šπ‘Ÿ2 NUM bibechana-46416 53 4 ] ] PUNCT bibechana-46416 53 5 πœ“(π‘Ÿ πœ“(π‘Ÿ NOUN bibechana-46416 53 6 ) ) PUNCT bibechana-46416 53 7 = = SYM bibechana-46416 53 8 0 0 PUNCT bibechana-46416 54 1 using use VERB bibechana-46416 54 2 centrifugal centrifugal ADJ bibechana-46416 54 3 approximation approximation NOUN bibechana-46416 54 4 1 1 NUM bibechana-46416 54 5 π‘Ÿ2 π‘Ÿ2 NOUN bibechana-46416 54 6 = = SYM bibechana-46416 54 7 4𝛼2π‘’βˆ’2π›Όπ‘Ÿ 4𝛼2π‘’βˆ’2π›Όπ‘Ÿ NUM bibechana-46416 54 8 ( ( PUNCT bibechana-46416 54 9 1βˆ’π‘’βˆ’2π›Όπ‘Ÿ)2 1βˆ’π‘’βˆ’2π›Όπ‘Ÿ)2 NUM bibechana-46416 54 10 , , PUNCT bibechana-46416 54 11 a a DET bibechana-46416 54 12 radical radical ADJ bibechana-46416 54 13 form form NOUN bibechana-46416 54 14 of of ADP bibechana-46416 54 15 se se ADV bibechana-46416 54 16 become become VERB bibechana-46416 54 17 πœ“β€²β€²(π‘Ÿ πœ“β€²β€²(π‘Ÿ NOUN bibechana-46416 54 18 ) ) PUNCT bibechana-46416 55 1 + + NUM bibechana-46416 55 2 2π‘š 2π‘š NUM bibechana-46416 55 3 ℏ2 ℏ2 NOUN bibechana-46416 55 4 [ [ X bibechana-46416 55 5 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 55 6 + + NUM bibechana-46416 55 7 𝑉0𝑒 𝑉0𝑒 PROPN bibechana-46416 55 8 βˆ’2π›Όπ‘Ÿ βˆ’2π›Όπ‘Ÿ VERB bibechana-46416 55 9 1 1 NUM bibechana-46416 55 10 βˆ’ βˆ’ NOUN bibechana-46416 55 11 π‘žπ‘’βˆ’2π›Όπ‘Ÿ π‘žπ‘’βˆ’2π›Όπ‘Ÿ ADP bibechana-46416 55 12 βˆ’ βˆ’ PROPN bibechana-46416 55 13 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 56 1 + + CCONJ bibechana-46416 56 2 1)ℏ2 1)ℏ2 NUM bibechana-46416 56 3 2π‘š 2π‘š NOUN bibechana-46416 56 4 4𝛼2π‘’βˆ’2π›Όπ‘Ÿ 4𝛼2π‘’βˆ’2π›Όπ‘Ÿ NUM bibechana-46416 56 5 ( ( PUNCT bibechana-46416 56 6 1 1 NUM bibechana-46416 56 7 βˆ’ βˆ’ PROPN bibechana-46416 56 8 π‘’βˆ’2π›Όπ‘Ÿ)2 π‘’βˆ’2π›Όπ‘Ÿ)2 PROPN bibechana-46416 56 9 ] ] PUNCT bibechana-46416 56 10 πœ“(π‘Ÿ πœ“(π‘Ÿ PROPN bibechana-46416 56 11 ) ) PUNCT bibechana-46416 56 12 = = SYM bibechana-46416 56 13 0 0 PUNCT bibechana-46416 56 14 let let VERB bibechana-46416 56 15 us we PRON bibechana-46416 56 16 consider consider VERB bibechana-46416 56 17 𝑍 𝑍 NOUN bibechana-46416 56 18 = = SYM bibechana-46416 56 19 1 1 NUM bibechana-46416 56 20 1βˆ’π‘’βˆ’2π›Όπ‘Ÿ 1βˆ’π‘’βˆ’2π›Όπ‘Ÿ NOUN bibechana-46416 56 21 then then ADV bibechana-46416 56 22 the the DET bibechana-46416 56 23 radial radial ADJ bibechana-46416 56 24 form form NOUN bibechana-46416 56 25 of of ADP bibechana-46416 56 26 the the DET bibechana-46416 56 27 equation equation NOUN bibechana-46416 56 28 become become VERB bibechana-46416 56 29 πœ“β€²β€²(π‘Ÿ πœ“β€²β€²(π‘Ÿ ADJ bibechana-46416 56 30 ) ) PUNCT bibechana-46416 57 1 + + NUM bibechana-46416 57 2 2π‘š 2π‘š NUM bibechana-46416 57 3 ℏ2 ℏ2 NOUN bibechana-46416 57 4 [ [ X bibechana-46416 57 5 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 57 6 + + NUM bibechana-46416 57 7 𝑉0 𝑉0 NOUN bibechana-46416 57 8 ( ( PUNCT bibechana-46416 57 9 𝑍 𝑍 PROPN bibechana-46416 57 10 βˆ’ βˆ’ NOUN bibechana-46416 57 11 1 1 NUM bibechana-46416 57 12 ) ) PUNCT bibechana-46416 57 13 βˆ’ βˆ’ PROPN bibechana-46416 58 1 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 59 1 + + CCONJ bibechana-46416 59 2 1)ℏ2 1)ℏ2 NUM bibechana-46416 59 3 2π‘š 2π‘š NOUN bibechana-46416 59 4 𝑍24𝛼2 𝑍24𝛼2 PROPN bibechana-46416 59 5 ( ( PUNCT bibechana-46416 59 6 𝑍 𝑍 PROPN bibechana-46416 59 7 βˆ’ βˆ’ NOUN bibechana-46416 59 8 1 1 NUM bibechana-46416 59 9 ) ) PUNCT bibechana-46416 59 10 𝑍 𝑍 VERB bibechana-46416 59 11 ] ] PUNCT bibechana-46416 59 12 πœ“(π‘Ÿ πœ“(π‘Ÿ NOUN bibechana-46416 59 13 ) ) PUNCT bibechana-46416 59 14 = = SYM bibechana-46416 59 15 0 0 PUNCT bibechana-46416 59 16 ( ( PUNCT bibechana-46416 59 17 1 1 NUM bibechana-46416 59 18 ) ) PUNCT bibechana-46416 59 19 on on ADP bibechana-46416 59 20 solving solve VERB bibechana-46416 59 21 equation equation NOUN bibechana-46416 59 22 ( ( PUNCT bibechana-46416 59 23 1 1 NUM bibechana-46416 59 24 ) ) PUNCT bibechana-46416 59 25 , , PUNCT bibechana-46416 59 26 we we PRON bibechana-46416 59 27 get get VERB bibechana-46416 59 28 πœ“β€²β€²(𝑍 πœ“β€²β€²(𝑍 NOUN bibechana-46416 59 29 ) ) PUNCT bibechana-46416 59 30 𝑍(𝑍 𝑍(𝑍 PROPN bibechana-46416 59 31 βˆ’ βˆ’ PROPN bibechana-46416 59 32 1 1 X bibechana-46416 59 33 ) ) PUNCT bibechana-46416 60 1 + + NUM bibechana-46416 60 2 πœ“β€²(𝑍)(2𝑍 πœ“β€²(𝑍)(2𝑍 NOUN bibechana-46416 60 3 βˆ’ βˆ’ NOUN bibechana-46416 60 4 1 1 X bibechana-46416 60 5 ) ) PUNCT bibechana-46416 61 1 + + CCONJ bibechana-46416 61 2 [ [ PUNCT bibechana-46416 61 3 π‘šπΈπ‘›π‘™ π‘šπΈπ‘›π‘™ PROPN bibechana-46416 61 4 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 61 5 1 1 NUM bibechana-46416 61 6 𝑍(𝑍 𝑍(𝑍 NOUN bibechana-46416 61 7 βˆ’ βˆ’ PROPN bibechana-46416 61 8 1 1 NUM bibechana-46416 61 9 ) ) PUNCT bibechana-46416 61 10 + + CCONJ bibechana-46416 61 11 π‘šπ‘‰0 π‘šπ‘‰0 ADP bibechana-46416 61 12 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 61 13 1 1 NUM bibechana-46416 61 14 𝑍 𝑍 PROPN bibechana-46416 61 15 βˆ’ βˆ’ NOUN bibechana-46416 61 16 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 61 17 + + NUM bibechana-46416 61 18 1)]πœ“(𝑍 1)]πœ“(𝑍 NUM bibechana-46416 61 19 ) ) PUNCT bibechana-46416 61 20 = = SYM bibechana-46416 61 21 0 0 PUNCT bibechana-46416 61 22 ( ( PUNCT bibechana-46416 61 23 2 2 NUM bibechana-46416 61 24 ) ) PUNCT bibechana-46416 61 25 again again ADV bibechana-46416 61 26 supposed suppose VERB bibechana-46416 61 27 π‘šπΈπ‘›π‘™ π‘šπΈπ‘›π‘™ PROPN bibechana-46416 61 28 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 61 29 = = SYM bibechana-46416 61 30 βˆ’πœ– βˆ’πœ– NOUN bibechana-46416 61 31 , , PUNCT bibechana-46416 61 32 𝛿 𝛿 ADJ bibechana-46416 61 33 = = SYM bibechana-46416 61 34 π‘šπ‘‰0 π‘šπ‘‰0 PROPN bibechana-46416 61 35 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 61 36 , , PUNCT bibechana-46416 61 37 𝜁 𝜁 PROPN bibechana-46416 61 38 = = SYM bibechana-46416 61 39 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 62 1 + + NOUN bibechana-46416 62 2 1 1 NUM bibechana-46416 62 3 ) ) PUNCT bibechana-46416 63 1 , , PUNCT bibechana-46416 63 2 therefore therefore ADV bibechana-46416 63 3 equation equation NOUN bibechana-46416 63 4 ( ( PUNCT bibechana-46416 63 5 2 2 X bibechana-46416 63 6 ) ) PUNCT bibechana-46416 63 7 becomes become VERB bibechana-46416 63 8 πœ“β€²β€²(𝑍 πœ“β€²β€²(𝑍 NOUN bibechana-46416 63 9 ) ) PUNCT bibechana-46416 63 10 𝑍(1 𝑍(1 PUNCT bibechana-46416 63 11 βˆ’ βˆ’ PROPN bibechana-46416 63 12 𝑍 𝑍 NOUN bibechana-46416 63 13 ) ) PUNCT bibechana-46416 63 14 + + NUM bibechana-46416 63 15 πœ“β€²(𝑍)(1 πœ“β€²(𝑍)(1 NOUN bibechana-46416 63 16 βˆ’ βˆ’ NOUN bibechana-46416 63 17 2𝑍 2𝑍 NOUN bibechana-46416 63 18 ) ) PUNCT bibechana-46416 64 1 + + CCONJ bibechana-46416 64 2 [ [ PUNCT bibechana-46416 64 3 βˆ’πœ– βˆ’πœ– NOUN bibechana-46416 64 4 𝑍(𝑍 𝑍(𝑍 PROPN bibechana-46416 64 5 βˆ’ βˆ’ PROPN bibechana-46416 64 6 1 1 NUM bibechana-46416 64 7 ) ) PUNCT bibechana-46416 64 8 βˆ’ βˆ’ NOUN bibechana-46416 64 9 𝛿 𝛿 DET bibechana-46416 64 10 𝑍 𝑍 NOUN bibechana-46416 64 11 + + CCONJ bibechana-46416 64 12 𝜁]πœ“(𝑍 𝜁]πœ“(𝑍 NOUN bibechana-46416 64 13 ) ) PUNCT bibechana-46416 64 14 = = SYM bibechana-46416 64 15 0 0 PUNCT bibechana-46416 64 16 ( ( PUNCT bibechana-46416 64 17 3 3 NUM bibechana-46416 64 18 ) ) PUNCT bibechana-46416 64 19 now now ADV bibechana-46416 64 20 asymptotic asymptotic ADJ bibechana-46416 64 21 behavior behavior NOUN bibechana-46416 64 22 of of ADP bibechana-46416 64 23 equation equation NOUN bibechana-46416 64 24 ( ( PUNCT bibechana-46416 64 25 3 3 NUM bibechana-46416 64 26 ) ) PUNCT bibechana-46416 64 27 , , PUNCT bibechana-46416 64 28 at at ADP bibechana-46416 64 29 π‘Ÿ π‘Ÿ NOUN bibechana-46416 64 30 β†’ β†’ SYM bibechana-46416 64 31 0 0 NUM bibechana-46416 64 32 ( ( PUNCT bibechana-46416 64 33 𝑍 𝑍 PROPN bibechana-46416 64 34 β†’ β†’ SYM bibechana-46416 64 35 1 1 NUM bibechana-46416 64 36 ) ) PUNCT bibechana-46416 64 37 and and CCONJ bibechana-46416 64 38 π‘Ÿ π‘Ÿ NOUN bibechana-46416 64 39 β†’ β†’ SYM bibechana-46416 64 40 ∞ ∞ PROPN bibechana-46416 64 41 ( ( PUNCT bibechana-46416 64 42 𝑍 𝑍 PROPN bibechana-46416 64 43 β†’ β†’ SYM bibechana-46416 64 44 0 0 NUM bibechana-46416 64 45 ) ) PUNCT bibechana-46416 64 46 , , PUNCT bibechana-46416 64 47 let let VERB bibechana-46416 64 48 us we PRON bibechana-46416 64 49 introduce introduce VERB bibechana-46416 64 50 a a DET bibechana-46416 64 51 new new ADJ bibechana-46416 64 52 function function NOUN bibechana-46416 64 53 𝑓(𝑍 𝑓(𝑍 PROPN bibechana-46416 64 54 ) ) PUNCT bibechana-46416 64 55 as as ADP bibechana-46416 64 56 πœ“(𝑍 πœ“(𝑍 X bibechana-46416 64 57 ) ) PUNCT bibechana-46416 64 58 = = PUNCT bibechana-46416 64 59 π‘πœ‡(1 π‘πœ‡(1 ADJ bibechana-46416 64 60 βˆ’ βˆ’ PROPN bibechana-46416 64 61 𝑍)πœ™π‘“(𝑍 𝑍)πœ™π‘“(𝑍 NOUN bibechana-46416 64 62 ) ) PUNCT bibechana-46416 64 63 ( ( PUNCT bibechana-46416 64 64 4 4 X bibechana-46416 64 65 ) ) PUNCT bibechana-46416 64 66 combining combine VERB bibechana-46416 64 67 equations equation NOUN bibechana-46416 64 68 ( ( PUNCT bibechana-46416 64 69 4 4 NUM bibechana-46416 64 70 ) ) PUNCT bibechana-46416 64 71 and and CCONJ bibechana-46416 64 72 ( ( PUNCT bibechana-46416 64 73 3 3 NUM bibechana-46416 64 74 ) ) PUNCT bibechana-46416 64 75 , , PUNCT bibechana-46416 64 76 we we PRON bibechana-46416 64 77 get get VERB bibechana-46416 64 78 a a DET bibechana-46416 64 79 new new ADJ bibechana-46416 64 80 equation equation NOUN bibechana-46416 64 81 of of ADP bibechana-46416 64 82 the the DET bibechana-46416 64 83 form form NOUN bibechana-46416 64 84 𝑍(1 𝑍(1 PUNCT bibechana-46416 64 85 βˆ’ βˆ’ NUM bibechana-46416 64 86 𝑍)𝑓′′(𝑍 𝑍)𝑓′′(𝑍 PROPN bibechana-46416 64 87 ) ) PUNCT bibechana-46416 65 1 + + CCONJ bibechana-46416 66 1 [ [ X bibechana-46416 66 2 1 1 NUM bibechana-46416 66 3 + + NUM bibechana-46416 66 4 2πœ‡ 2πœ‡ NUM bibechana-46416 66 5 βˆ’ βˆ’ PROPN bibechana-46416 66 6 ( ( PUNCT bibechana-46416 66 7 2πœ‡ 2πœ‡ NOUN bibechana-46416 66 8 βˆ’ βˆ’ NOUN bibechana-46416 66 9 2πœ™ 2πœ™ NOUN bibechana-46416 66 10 βˆ’ βˆ’ PROPN bibechana-46416 66 11 2)𝑍]𝑓′(𝑍 2)𝑍]𝑓′(𝑍 NUM bibechana-46416 66 12 ) ) PUNCT bibechana-46416 66 13 βˆ’ βˆ’ PROPN bibechana-46416 67 1 [ [ X bibechana-46416 67 2 ( ( PUNCT bibechana-46416 67 3 πœ‡ πœ‡ X bibechana-46416 67 4 + + NOUN bibechana-46416 67 5 πœ™)2 πœ™)2 NOUN bibechana-46416 67 6 + + CCONJ bibechana-46416 67 7 ( ( PUNCT bibechana-46416 67 8 πœ‡ πœ‡ X bibechana-46416 67 9 + + X bibechana-46416 67 10 πœ™ πœ™ NOUN bibechana-46416 67 11 ) ) PUNCT bibechana-46416 67 12 + + CCONJ bibechana-46416 67 13 𝜁)]𝑓(𝑍 𝜁)]𝑓(𝑍 NOUN bibechana-46416 67 14 ) ) PUNCT bibechana-46416 67 15 + + CCONJ bibechana-46416 67 16 [ [ PUNCT bibechana-46416 67 17 βˆ’πœ– βˆ’πœ– NOUN bibechana-46416 67 18 βˆ’ βˆ’ PROPN bibechana-46416 67 19 𝛿 𝛿 ADJ bibechana-46416 67 20 + + NUM bibechana-46416 67 21 ΞΌ2 ΞΌ2 NOUN bibechana-46416 67 22 𝑍(1 𝑍(1 PUNCT bibechana-46416 67 23 βˆ’ βˆ’ PROPN bibechana-46416 67 24 𝑍 𝑍 PROPN bibechana-46416 67 25 ) ) PUNCT bibechana-46416 67 26 + + NUM bibechana-46416 67 27 πœ™2 πœ™2 NOUN bibechana-46416 67 28 βˆ’ βˆ’ PROPN bibechana-46416 67 29 πœ‡2 πœ‡2 PROPN bibechana-46416 67 30 + + CCONJ bibechana-46416 67 31 𝛿 𝛿 X bibechana-46416 67 32 ( ( PUNCT bibechana-46416 67 33 1 1 NUM bibechana-46416 67 34 βˆ’ βˆ’ PROPN bibechana-46416 67 35 𝑍 𝑍 NOUN bibechana-46416 67 36 ) ) PUNCT bibechana-46416 67 37 ] ] SYM bibechana-46416 67 38 𝑓(𝑍 𝑓(𝑍 PROPN bibechana-46416 67 39 ) ) PUNCT bibechana-46416 68 1 = = SYM bibechana-46416 68 2 0 0 PUNCT bibechana-46416 68 3 ( ( PUNCT bibechana-46416 68 4 5 5 NUM bibechana-46416 68 5 ) ) PUNCT bibechana-46416 68 6 now now ADV bibechana-46416 68 7 equation equation NOUN bibechana-46416 68 8 ( ( PUNCT bibechana-46416 68 9 5 5 NUM bibechana-46416 68 10 ) ) PUNCT bibechana-46416 68 11 becomes become VERB bibechana-46416 68 12 the the DET bibechana-46416 68 13 gauss gauss ADJ bibechana-46416 68 14 hypergeometric hypergeometric ADJ bibechana-46416 68 15 equation equation NOUN bibechana-46416 68 16 when when SCONJ bibechana-46416 68 17 the the DET bibechana-46416 68 18 square square ADJ bibechana-46416 68 19 bracket bracket ADJ bibechana-46416 68 20 term term NOUN bibechana-46416 68 21 equal equal ADJ bibechana-46416 68 22 to to ADP bibechana-46416 68 23 zero zero NUM bibechana-46416 68 24 βˆ’πœ– βˆ’πœ– NOUN bibechana-46416 68 25 βˆ’ βˆ’ PROPN bibechana-46416 68 26 𝛿 𝛿 PROPN bibechana-46416 68 27 + + PROPN bibechana-46416 68 28 ΞΌ2 ΞΌ2 NOUN bibechana-46416 68 29 = = SYM bibechana-46416 68 30 0 0 NUM bibechana-46416 68 31 , , PUNCT bibechana-46416 68 32 πœ™2 πœ™2 NOUN bibechana-46416 68 33 βˆ’ βˆ’ PROPN bibechana-46416 68 34 πœ‡2 πœ‡2 PROPN bibechana-46416 68 35 + + CCONJ bibechana-46416 68 36 𝛿 𝛿 ADJ bibechana-46416 68 37 = = SYM bibechana-46416 68 38 0 0 NUM bibechana-46416 68 39 karki karki NOUN bibechana-46416 68 40 et et PROPN bibechana-46416 68 41 al al PROPN bibechana-46416 68 42 . . PUNCT bibechana-46416 68 43 / / SYM bibechana-46416 68 44 bibechana bibechana PROPN bibechana-46416 68 45 19(1 19(1 NUM bibechana-46416 68 46 - - SYM bibechana-46416 68 47 2 2 NUM bibechana-46416 68 48 ) ) PUNCT bibechana-46416 68 49 ( ( PUNCT bibechana-46416 68 50 2022 2022 NUM bibechana-46416 68 51 ) ) PUNCT bibechana-46416 68 52 165 165 NUM bibechana-46416 68 53 - - SYM bibechana-46416 68 54 169 169 NUM bibechana-46416 68 55 167 167 NUM bibechana-46416 68 56 therefore therefore ADV bibechana-46416 68 57 , , PUNCT bibechana-46416 68 58 equation equation NOUN bibechana-46416 68 59 ( ( PUNCT bibechana-46416 68 60 5 5 NUM bibechana-46416 68 61 ) ) PUNCT bibechana-46416 68 62 is be AUX bibechana-46416 68 63 written write VERB bibechana-46416 68 64 as as ADP bibechana-46416 68 65 𝑍(1 𝑍(1 PUNCT bibechana-46416 68 66 βˆ’ βˆ’ PROPN bibechana-46416 68 67 𝑍)𝑓′′(𝑍 𝑍)𝑓′′(𝑍 PROPN bibechana-46416 68 68 ) ) PUNCT bibechana-46416 69 1 + + CCONJ bibechana-46416 70 1 [ [ X bibechana-46416 70 2 1 1 NUM bibechana-46416 70 3 + + NUM bibechana-46416 70 4 2πœ‡ 2πœ‡ NUM bibechana-46416 70 5 βˆ’ βˆ’ PROPN bibechana-46416 70 6 ( ( PUNCT bibechana-46416 70 7 2πœ‡ 2πœ‡ NOUN bibechana-46416 70 8 βˆ’ βˆ’ NOUN bibechana-46416 70 9 2πœ™ 2πœ™ NOUN bibechana-46416 70 10 βˆ’ βˆ’ PROPN bibechana-46416 70 11 2)𝑍]𝑓′(𝑍 2)𝑍]𝑓′(𝑍 NUM bibechana-46416 70 12 ) ) PUNCT bibechana-46416 70 13 βˆ’ βˆ’ PROPN bibechana-46416 71 1 [ [ X bibechana-46416 71 2 ( ( PUNCT bibechana-46416 71 3 πœ‡ πœ‡ ADP bibechana-46416 71 4 + + NOUN bibechana-46416 71 5 πœ™ πœ™ NOUN bibechana-46416 71 6 + + NOUN bibechana-46416 71 7 1 1 NUM bibechana-46416 71 8 2 2 NUM bibechana-46416 71 9 + + CCONJ bibechana-46416 71 10 √ √ NUM bibechana-46416 71 11 1 1 NUM bibechana-46416 71 12 4 4 NUM bibechana-46416 71 13 βˆ’ βˆ’ PROPN bibechana-46416 71 14 𝜁 𝜁 PROPN bibechana-46416 71 15 ) ) PUNCT bibechana-46416 71 16 Γ— Γ— NOUN bibechana-46416 71 17 ( ( PUNCT bibechana-46416 71 18 πœ‡ πœ‡ X bibechana-46416 71 19 + + NOUN bibechana-46416 71 20 πœ™ πœ™ NOUN bibechana-46416 71 21 + + NOUN bibechana-46416 71 22 1 1 NUM bibechana-46416 71 23 2 2 NUM bibechana-46416 71 24 βˆ’ βˆ’ NOUN bibechana-46416 71 25 √ √ NOUN bibechana-46416 71 26 1 1 NUM bibechana-46416 71 27 4 4 NUM bibechana-46416 71 28 βˆ’ βˆ’ NOUN bibechana-46416 71 29 𝜁)]𝑓(𝑍 𝜁)]𝑓(𝑍 NOUN bibechana-46416 71 30 ) ) PUNCT bibechana-46416 71 31 = = SYM bibechana-46416 71 32 0 0 NUM bibechana-46416 71 33 ( ( PUNCT bibechana-46416 71 34 6 6 NUM bibechana-46416 71 35 ) ) PUNCT bibechana-46416 71 36 the the DET bibechana-46416 71 37 gaussian gaussian ADJ bibechana-46416 71 38 hypergeometric hypergeometric ADJ bibechana-46416 71 39 function function NOUN bibechana-46416 71 40 ( ( PUNCT bibechana-46416 71 41 ghf ghf PROPN bibechana-46416 71 42 ) ) PUNCT bibechana-46416 71 43 , , PUNCT bibechana-46416 71 44 2f1(π‘Ž 2f1(π‘Ž NUM bibechana-46416 71 45 , , PUNCT bibechana-46416 71 46 𝑏 𝑏 NOUN bibechana-46416 71 47 ; ; PUNCT bibechana-46416 71 48 𝑐 𝑐 NUM bibechana-46416 71 49 ; ; PUNCT bibechana-46416 71 50 𝑧 𝑧 X bibechana-46416 71 51 ) ) PUNCT bibechana-46416 71 52 can can AUX bibechana-46416 71 53 be be AUX bibechana-46416 71 54 expressed express VERB bibechana-46416 71 55 as as ADP bibechana-46416 71 56 infinite infinite ADJ bibechana-46416 71 57 series series NOUN bibechana-46416 71 58 for for ADP bibechana-46416 71 59 |𝑧| |𝑧| PROPN bibechana-46416 71 60 < < X bibechana-46416 71 61 1 1 NUM bibechana-46416 71 62 as as ADP bibechana-46416 71 63 , , PUNCT bibechana-46416 71 64 2f1(π‘Ž 2f1(π‘Ž NUM bibechana-46416 71 65 , , PUNCT bibechana-46416 71 66 𝑏 𝑏 NOUN bibechana-46416 71 67 ; ; PUNCT bibechana-46416 71 68 𝑐 𝑐 NUM bibechana-46416 71 69 ; ; PUNCT bibechana-46416 71 70 𝑧 𝑧 X bibechana-46416 71 71 ) ) PUNCT bibechana-46416 71 72 = = SYM bibechana-46416 71 73 βˆ‘ βˆ‘ PUNCT bibechana-46416 71 74 ( ( PUNCT bibechana-46416 71 75 π‘Ž)𝑛(𝑏)𝑛 π‘Ž)𝑛(𝑏)𝑛 PROPN bibechana-46416 71 76 ( ( PUNCT bibechana-46416 71 77 𝑐)𝑛 𝑐)𝑛 NOUN bibechana-46416 71 78 ∞ ∞ NUM bibechana-46416 71 79 𝑛=0 𝑛=0 PROPN bibechana-46416 71 80 𝑧𝑛 𝑧𝑛 VERB bibechana-46416 71 81 𝑛 𝑛 PROPN bibechana-46416 71 82 ! ! PUNCT bibechana-46416 71 83 = = NOUN bibechana-46416 72 1 1 1 NUM bibechana-46416 72 2 + + CCONJ bibechana-46416 72 3 π‘Žπ‘ π‘Žπ‘ PROPN bibechana-46416 72 4 𝑐 𝑐 NOUN bibechana-46416 72 5 𝑧 𝑧 PROPN bibechana-46416 72 6 1 1 NUM bibechana-46416 72 7 ! ! PUNCT bibechana-46416 73 1 + + NUM bibechana-46416 73 2 π‘Ž(π‘Ž+1)𝑏(𝑏+1 π‘Ž(π‘Ž+1)𝑏(𝑏+1 PROPN bibechana-46416 73 3 ) ) PUNCT bibechana-46416 73 4 𝑐(𝑐+1 𝑐(𝑐+1 NOUN bibechana-46416 73 5 ) ) PUNCT bibechana-46416 73 6 𝑧2 𝑧2 NOUN bibechana-46416 73 7 2 2 NUM bibechana-46416 73 8 ! ! PUNCT bibechana-46416 74 1 + + VERB bibechana-46416 74 2 β‹― β‹― NOUN bibechana-46416 74 3 …… …… NOUN bibechana-46416 74 4 . . PUNCT bibechana-46416 75 1 here here ADV bibechana-46416 75 2 ( ( PUNCT bibechana-46416 75 3 π‘Ž)𝑛 π‘Ž)𝑛 X bibechana-46416 75 4 ≔ ≔ NOUN bibechana-46416 75 5 Ξ³(π‘Ž+𝑛 Ξ³(π‘Ž+𝑛 NOUN bibechana-46416 75 6 ) ) PUNCT bibechana-46416 75 7 Ξ³(π‘Ž Ξ³(π‘Ž PROPN bibechana-46416 75 8 ) ) PUNCT bibechana-46416 75 9 , , PUNCT bibechana-46416 75 10 ( ( PUNCT bibechana-46416 75 11 𝑏)𝑛 𝑏)𝑛 X bibechana-46416 75 12 ≔ ≔ VERB bibechana-46416 75 13 Ξ³(𝑏+𝑛 Ξ³(𝑏+𝑛 ADJ bibechana-46416 75 14 ) ) PUNCT bibechana-46416 75 15 Ξ³(𝑏 Ξ³(𝑏 NOUN bibechana-46416 75 16 ) ) PUNCT bibechana-46416 75 17 , , PUNCT bibechana-46416 75 18 ( ( PUNCT bibechana-46416 75 19 𝑐)𝑛 𝑐)𝑛 NOUN bibechana-46416 75 20 ≔ ≔ NOUN bibechana-46416 75 21 Ξ³(𝑐+𝑛 Ξ³(𝑐+𝑛 NOUN bibechana-46416 75 22 ) ) PUNCT bibechana-46416 75 23 Ξ³(𝑐 Ξ³(𝑐 PROPN bibechana-46416 75 24 ) ) PUNCT bibechana-46416 75 25 putting put VERB bibechana-46416 75 26 these these PRON bibechana-46416 75 27 in in ADP bibechana-46416 75 28 the the DET bibechana-46416 75 29 above above ADJ bibechana-46416 75 30 equation equation NOUN bibechana-46416 75 31 and and CCONJ bibechana-46416 75 32 simplifying simplify VERB bibechana-46416 75 33 we we PRON bibechana-46416 75 34 get get VERB bibechana-46416 75 35 , , PUNCT bibechana-46416 75 36 𝑓(𝑍 𝑓(𝑍 PROPN bibechana-46416 75 37 ) ) PUNCT bibechana-46416 76 1 = = PUNCT bibechana-46416 76 2 𝐹1(π‘Ž1 𝐹1(π‘Ž1 PROPN bibechana-46416 76 3 , , PUNCT bibechana-46416 76 4 𝑏2 𝑏2 PROPN bibechana-46416 76 5 ; ; PUNCT bibechana-46416 76 6 𝑐1 𝑐1 NOUN bibechana-46416 76 7 ; ; PUNCT bibechana-46416 76 8 𝑍)2 𝑍)2 NUM bibechana-46416 76 9 = = SYM bibechana-46416 76 10 Ξ³(𝑐1 Ξ³(𝑐1 NUM bibechana-46416 76 11 ) ) PUNCT bibechana-46416 76 12 Ξ³(π‘Ž1)Ξ³(𝑏1 Ξ³(π‘Ž1)Ξ³(𝑏1 NOUN bibechana-46416 76 13 ) ) PUNCT bibechana-46416 76 14 here here ADV bibechana-46416 76 15 we we PRON bibechana-46416 76 16 consider consider VERB bibechana-46416 76 17 π‘Ž1 π‘Ž1 ADJ bibechana-46416 76 18 , , PUNCT bibechana-46416 76 19 , , PUNCT bibechana-46416 76 20 𝑏1 𝑏1 NOUN bibechana-46416 76 21 and and CCONJ bibechana-46416 76 22 𝑐1 𝑐1 NOUN bibechana-46416 76 23 are be AUX bibechana-46416 76 24 unknown unknown ADJ bibechana-46416 76 25 parameters parameter NOUN bibechana-46416 76 26 whose whose DET bibechana-46416 76 27 values value NOUN bibechana-46416 76 28 are be AUX bibechana-46416 76 29 expressed express VERB bibechana-46416 76 30 as as ADP bibechana-46416 76 31 π‘Ž1 π‘Ž1 PROPN bibechana-46416 76 32 = = PUNCT bibechana-46416 76 33 ( ( PUNCT bibechana-46416 76 34 πœ‡ πœ‡ X bibechana-46416 76 35 + + NOUN bibechana-46416 76 36 πœ™ πœ™ NOUN bibechana-46416 76 37 + + NOUN bibechana-46416 76 38 1 1 NUM bibechana-46416 76 39 2 2 NUM bibechana-46416 76 40 + + CCONJ bibechana-46416 76 41 √ √ NUM bibechana-46416 76 42 1 1 NUM bibechana-46416 76 43 4 4 NUM bibechana-46416 76 44 βˆ’ βˆ’ PROPN bibechana-46416 76 45 𝜁 𝜁 NOUN bibechana-46416 76 46 ) ) PUNCT bibechana-46416 76 47 , , PUNCT bibechana-46416 76 48 𝑏1 𝑏1 NOUN bibechana-46416 76 49 = = SYM bibechana-46416 76 50 ( ( PUNCT bibechana-46416 76 51 πœ‡ πœ‡ X bibechana-46416 76 52 + + NOUN bibechana-46416 76 53 πœ™ πœ™ NOUN bibechana-46416 76 54 + + NOUN bibechana-46416 76 55 1 1 NUM bibechana-46416 76 56 2 2 NUM bibechana-46416 76 57 βˆ’ βˆ’ NOUN bibechana-46416 76 58 √ √ NOUN bibechana-46416 76 59 1 1 NUM bibechana-46416 76 60 4 4 NUM bibechana-46416 76 61 βˆ’ βˆ’ PROPN bibechana-46416 76 62 𝜁 𝜁 NOUN bibechana-46416 76 63 ) ) PUNCT bibechana-46416 76 64 , , PUNCT bibechana-46416 76 65 𝑐1 𝑐1 NOUN bibechana-46416 76 66 = = NOUN bibechana-46416 76 67 1 1 NUM bibechana-46416 76 68 + + NUM bibechana-46416 76 69 2πœ‡ 2πœ‡ NUM bibechana-46416 76 70 . . PUNCT bibechana-46416 77 1 now now ADV bibechana-46416 77 2 substituting substitute VERB bibechana-46416 77 3 the the DET bibechana-46416 77 4 value value NOUN bibechana-46416 77 5 of of ADP bibechana-46416 77 6 𝑓(𝑍 𝑓(𝑍 PROPN bibechana-46416 77 7 ) ) PUNCT bibechana-46416 77 8 with with ADP bibechana-46416 77 9 these these DET bibechana-46416 77 10 parameters parameter NOUN bibechana-46416 77 11 in in ADP bibechana-46416 77 12 πœ“(𝑍 πœ“(𝑍 NUM bibechana-46416 77 13 ) ) PUNCT bibechana-46416 77 14 = = PUNCT bibechana-46416 77 15 π‘πœ‡(1 π‘πœ‡(1 ADJ bibechana-46416 77 16 βˆ’ βˆ’ PROPN bibechana-46416 77 17 𝑍)πœ™π‘“(𝑍 𝑍)πœ™π‘“(𝑍 NOUN bibechana-46416 77 18 ) ) PUNCT bibechana-46416 77 19 in in ADP bibechana-46416 77 20 this this PRON bibechana-46416 77 21 , , PUNCT bibechana-46416 77 22 we we PRON bibechana-46416 77 23 get get VERB bibechana-46416 77 24 πœ“(𝑍 πœ“(𝑍 VERB bibechana-46416 77 25 ) ) PUNCT bibechana-46416 77 26 = = PUNCT bibechana-46416 78 1 π‘πœ‡(1 π‘πœ‡(1 NOUN bibechana-46416 78 2 βˆ’ βˆ’ X bibechana-46416 78 3 𝑍)πœ™ 𝑍)πœ™ X bibechana-46416 79 1 𝐹1(πœ‡ 𝐹1(πœ‡ PUNCT bibechana-46416 80 1 + + CCONJ bibechana-46416 80 2 πœ™ πœ™ PROPN bibechana-46416 80 3 + + NOUN bibechana-46416 80 4 1 1 NUM bibechana-46416 80 5 2 2 NUM bibechana-46416 80 6 + + CCONJ bibechana-46416 80 7 √ √ NUM bibechana-46416 80 8 1 1 NUM bibechana-46416 80 9 4 4 NUM bibechana-46416 80 10 βˆ’ βˆ’ PROPN bibechana-46416 80 11 𝜁 𝜁 PROPN bibechana-46416 80 12 , , PUNCT bibechana-46416 80 13 πœ‡ πœ‡ ADP bibechana-46416 80 14 + + NOUN bibechana-46416 80 15 πœ™ πœ™ NOUN bibechana-46416 80 16 + + NOUN bibechana-46416 80 17 1 1 NUM bibechana-46416 80 18 2 2 NUM bibechana-46416 80 19 βˆ’ βˆ’ NOUN bibechana-46416 80 20 √ √ NOUN bibechana-46416 80 21 1 1 NUM bibechana-46416 80 22 4 4 NUM bibechana-46416 80 23 βˆ’ βˆ’ NOUN bibechana-46416 80 24 𝜁 𝜁 NOUN bibechana-46416 80 25 ; ; PUNCT bibechana-46416 80 26 1 1 NUM bibechana-46416 80 27 + + NUM bibechana-46416 80 28 2πœ‡ 2πœ‡ NUM bibechana-46416 80 29 ; ; PUNCT bibechana-46416 80 30 𝑍)2 𝑍)2 NUM bibechana-46416 80 31 if if SCONJ bibechana-46416 80 32 π‘Ž1 π‘Ž1 ADV bibechana-46416 80 33 , , PUNCT bibechana-46416 80 34 𝑏1 𝑏1 ADJ bibechana-46416 80 35 , , PUNCT bibechana-46416 80 36 and and CCONJ bibechana-46416 80 37 𝑐1 𝑐1 NOUN bibechana-46416 80 38 is be AUX bibechana-46416 80 39 equal equal ADJ bibechana-46416 80 40 to to ADP bibechana-46416 80 41 the the DET bibechana-46416 80 42 negative negative NOUN bibechana-46416 80 43 of of ADP bibechana-46416 80 44 integer integer NOUN bibechana-46416 80 45 ( ( PUNCT bibechana-46416 80 46 𝑛 𝑛 NOUN bibechana-46416 80 47 ) ) PUNCT bibechana-46416 80 48 then then ADV bibechana-46416 80 49 hypergeometric hypergeometric ADJ bibechana-46416 80 50 function function NOUN bibechana-46416 80 51 𝑓(𝑍 𝑓(𝑍 PROPN bibechana-46416 80 52 ) ) PUNCT bibechana-46416 80 53 will will AUX bibechana-46416 80 54 become become VERB bibechana-46416 80 55 a a DET bibechana-46416 80 56 polynomial polynomial NOUN bibechana-46416 80 57 with with ADP bibechana-46416 80 58 𝑛 𝑛 PROPN bibechana-46416 80 59 = = SYM bibechana-46416 80 60 0 0 NUM bibechana-46416 80 61 , , PUNCT bibechana-46416 80 62 1 1 NUM bibechana-46416 80 63 , , PUNCT bibechana-46416 80 64 2 2 NUM bibechana-46416 80 65 , , PUNCT bibechana-46416 80 66 3 3 NUM bibechana-46416 80 67 , , PUNCT bibechana-46416 80 68 . . PUNCT bibechana-46416 80 69 . . PUNCT bibechana-46416 80 70 . . PUNCT bibechana-46416 81 1 , , PUNCT bibechana-46416 81 2 π‘›π‘šπ‘Žπ‘₯ π‘›π‘šπ‘Žπ‘₯ NOUN bibechana-46416 81 3 integer integer NOUN bibechana-46416 81 4 , , PUNCT bibechana-46416 81 5 applying apply VERB bibechana-46416 81 6 quantum quantum ADJ bibechana-46416 81 7 condition condition NOUN bibechana-46416 81 8 we we PRON bibechana-46416 81 9 have have VERB bibechana-46416 81 10 , , PUNCT bibechana-46416 81 11 π‘Ž1 π‘Ž1 ADJ bibechana-46416 81 12 = = PRON bibechana-46416 81 13 βˆ’π‘› βˆ’π‘› NOUN bibechana-46416 81 14 and and CCONJ bibechana-46416 81 15 𝑏1 𝑏1 ADJ bibechana-46416 81 16 = = SYM bibechana-46416 81 17 βˆ’π‘›. βˆ’π‘›. NOUN bibechana-46416 81 18 now now ADV bibechana-46416 81 19 using use VERB bibechana-46416 81 20 πœ™2βˆ’ πœ™2βˆ’ NOUN bibechana-46416 81 21 πœ‡2 πœ‡2 NOUN bibechana-46416 81 22 + + CCONJ bibechana-46416 81 23 𝛿 𝛿 ADJ bibechana-46416 81 24 = = SYM bibechana-46416 81 25 0 0 NUM bibechana-46416 81 26 to to PART bibechana-46416 81 27 calculate calculate VERB bibechana-46416 81 28 the the DET bibechana-46416 81 29 value value NOUN bibechana-46416 81 30 of of ADP bibechana-46416 81 31 πœ™ πœ™ PROPN bibechana-46416 81 32 and and CCONJ bibechana-46416 81 33 πœ‡ πœ‡ X bibechana-46416 81 34 from from ADP bibechana-46416 81 35 the the DET bibechana-46416 81 36 above above ADJ bibechana-46416 81 37 suitable suitable ADJ bibechana-46416 81 38 value value NOUN bibechana-46416 81 39 we we PRON bibechana-46416 81 40 get get VERB bibechana-46416 81 41 πœ™ πœ™ NOUN bibechana-46416 81 42 = = SYM bibechana-46416 81 43 ( ( PUNCT bibechana-46416 81 44 πœ”βˆ’π‘› πœ”βˆ’π‘› ADP bibechana-46416 81 45 2 2 NUM bibechana-46416 81 46 + + CCONJ bibechana-46416 81 47 𝛿 𝛿 ADJ bibechana-46416 81 48 2(πœ”βˆ’π‘› 2(πœ”βˆ’π‘› NUM bibechana-46416 81 49 ) ) PUNCT bibechana-46416 81 50 ) ) PUNCT bibechana-46416 81 51 and and CCONJ bibechana-46416 81 52 πœ‡ πœ‡ X bibechana-46416 81 53 = = X bibechana-46416 81 54 ( ( PUNCT bibechana-46416 81 55 πœ”βˆ’π‘› πœ”βˆ’π‘› ADP bibechana-46416 81 56 2 2 NUM bibechana-46416 81 57 βˆ’ βˆ’ NOUN bibechana-46416 81 58 𝛿 𝛿 PROPN bibechana-46416 81 59 2(πœ”βˆ’π‘› 2(πœ”βˆ’π‘› NOUN bibechana-46416 81 60 ) ) PUNCT bibechana-46416 81 61 ) ) PUNCT bibechana-46416 81 62 where where SCONJ bibechana-46416 81 63 πœ” πœ” PART bibechana-46416 81 64 = = PUNCT bibechana-46416 81 65 √ √ NUM bibechana-46416 81 66 1 1 NUM bibechana-46416 81 67 4 4 NUM bibechana-46416 81 68 βˆ’ βˆ’ NOUN bibechana-46416 81 69 𝜁 𝜁 PRON bibechana-46416 81 70 βˆ’ βˆ’ NUM bibechana-46416 81 71 1 1 NUM bibechana-46416 81 72 2 2 NUM bibechana-46416 81 73 = = NOUN bibechana-46416 81 74 πœ” πœ” NOUN bibechana-46416 81 75 now now ADV bibechana-46416 81 76 to to PART bibechana-46416 81 77 calculate calculate VERB bibechana-46416 81 78 the the DET bibechana-46416 81 79 energy energy NOUN bibechana-46416 81 80 we we PRON bibechana-46416 81 81 have have VERB bibechana-46416 81 82 from from ADP bibechana-46416 81 83 βˆ’πœ– βˆ’πœ– NOUN bibechana-46416 81 84 βˆ’ βˆ’ PROPN bibechana-46416 81 85 𝛿 𝛿 PROPN bibechana-46416 81 86 + + PROPN bibechana-46416 81 87 ΞΌ2 ΞΌ2 NOUN bibechana-46416 81 88 = = SYM bibechana-46416 81 89 0 0 NUM bibechana-46416 81 90 and and CCONJ bibechana-46416 81 91 πœ™2βˆ’ πœ™2βˆ’ PROPN bibechana-46416 81 92 πœ‡2 πœ‡2 NOUN bibechana-46416 81 93 + + CCONJ bibechana-46416 81 94 𝛿 𝛿 ADJ bibechana-46416 81 95 = = SYM bibechana-46416 81 96 0 0 NUM bibechana-46416 81 97 is be AUX bibechana-46416 81 98 πœ– πœ– PROPN bibechana-46416 81 99 = = PROPN bibechana-46416 81 100 πœ™2 πœ™2 PROPN bibechana-46416 81 101 . . PUNCT bibechana-46416 82 1 since since SCONJ bibechana-46416 82 2 we we PRON bibechana-46416 82 3 have have VERB bibechana-46416 82 4 π‘šπΈπ‘›π‘™ π‘šπΈπ‘›π‘™ PROPN bibechana-46416 82 5 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 82 6 = = SYM bibechana-46416 82 7 βˆ’πœ– βˆ’πœ– NOUN bibechana-46416 82 8 and and CCONJ bibechana-46416 82 9 πœ™ πœ™ NOUN bibechana-46416 82 10 = = SYM bibechana-46416 82 11 ( ( PUNCT bibechana-46416 82 12 πœ”βˆ’π‘› πœ”βˆ’π‘› ADP bibechana-46416 82 13 2 2 NUM bibechana-46416 82 14 + + CCONJ bibechana-46416 82 15 𝛿 𝛿 ADJ bibechana-46416 82 16 2(πœ”βˆ’π‘› 2(πœ”βˆ’π‘› NUM bibechana-46416 82 17 ) ) PUNCT bibechana-46416 82 18 ) ) PUNCT bibechana-46416 82 19 , , PUNCT bibechana-46416 82 20 therefore therefore ADV bibechana-46416 82 21 we we PRON bibechana-46416 82 22 have have VERB bibechana-46416 82 23 , , PUNCT bibechana-46416 82 24 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 82 25 = = PUNCT bibechana-46416 82 26 βˆ’ βˆ’ PROPN bibechana-46416 82 27 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 82 28 π‘š π‘š X bibechana-46416 82 29 ( ( PUNCT bibechana-46416 82 30 πœ” πœ” PROPN bibechana-46416 82 31 βˆ’ βˆ’ NOUN bibechana-46416 82 32 𝑛 𝑛 DET bibechana-46416 82 33 2 2 NUM bibechana-46416 82 34 + + CCONJ bibechana-46416 82 35 𝛿 𝛿 DET bibechana-46416 82 36 2(πœ” 2(πœ” NUM bibechana-46416 82 37 βˆ’ βˆ’ NOUN bibechana-46416 82 38 𝑛 𝑛 NOUN bibechana-46416 82 39 ) ) PUNCT bibechana-46416 82 40 ) ) PUNCT bibechana-46416 82 41 2 2 NUM bibechana-46416 82 42 ( ( PUNCT bibechana-46416 82 43 7 7 NUM bibechana-46416 82 44 ) ) PUNCT bibechana-46416 82 45 substituting substitute VERB bibechana-46416 82 46 the the DET bibechana-46416 82 47 value value NOUN bibechana-46416 82 48 of of ADP bibechana-46416 82 49 𝛿,πœ” 𝛿,πœ” PROPN bibechana-46416 82 50 , , PUNCT bibechana-46416 82 51 𝜁 𝜁 NOUN bibechana-46416 82 52 in in ADP bibechana-46416 82 53 equation equation NOUN bibechana-46416 82 54 ( ( PUNCT bibechana-46416 82 55 7 7 X bibechana-46416 82 56 ) ) PUNCT bibechana-46416 82 57 we we PRON bibechana-46416 82 58 get get VERB bibechana-46416 82 59 , , PUNCT bibechana-46416 83 1 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 83 2 = = PUNCT bibechana-46416 83 3 βˆ’ βˆ’ PROPN bibechana-46416 83 4 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 83 5 π‘š π‘š X bibechana-46416 83 6 ( ( PUNCT bibechana-46416 83 7 √ √ PROPN bibechana-46416 83 8 1 1 NUM bibechana-46416 83 9 4 4 NUM bibechana-46416 83 10 βˆ’ βˆ’ NOUN bibechana-46416 83 11 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 84 1 + + ADP bibechana-46416 84 2 1 1 X bibechana-46416 84 3 ) ) PUNCT bibechana-46416 84 4 βˆ’ βˆ’ NOUN bibechana-46416 85 1 1 1 NUM bibechana-46416 85 2 2 2 NUM bibechana-46416 85 3 βˆ’ βˆ’ NOUN bibechana-46416 85 4 𝑛 𝑛 DET bibechana-46416 85 5 2 2 NUM bibechana-46416 85 6 + + CCONJ bibechana-46416 85 7 π‘šπ‘‰0 π‘šπ‘‰0 PROPN bibechana-46416 85 8 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 85 9 2(√ 2(√ NUM bibechana-46416 85 10 1 1 NUM bibechana-46416 85 11 4 4 NUM bibechana-46416 85 12 βˆ’ βˆ’ NOUN bibechana-46416 85 13 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 86 1 + + ADP bibechana-46416 86 2 1 1 X bibechana-46416 86 3 ) ) PUNCT bibechana-46416 86 4 βˆ’ βˆ’ NOUN bibechana-46416 87 1 1 1 NUM bibechana-46416 87 2 2 2 NUM bibechana-46416 87 3 βˆ’ βˆ’ NUM bibechana-46416 87 4 𝑛 𝑛 NOUN bibechana-46416 87 5 ) ) PUNCT bibechana-46416 87 6 ) ) PUNCT bibechana-46416 88 1 2 2 NUM bibechana-46416 89 1 𝐸𝑛𝑙 𝐸𝑛𝑙 NOUN bibechana-46416 89 2 = = PUNCT bibechana-46416 89 3 βˆ’ βˆ’ NOUN bibechana-46416 89 4 ℏ2𝛼2 ℏ2𝛼2 NOUN bibechana-46416 89 5 2π‘š 2π‘š NOUN bibechana-46416 89 6 ( ( PUNCT bibechana-46416 89 7 ( ( PUNCT bibechana-46416 89 8 √ √ NUM bibechana-46416 89 9 1 1 NUM bibechana-46416 89 10 4 4 NUM bibechana-46416 89 11 βˆ’ βˆ’ NOUN bibechana-46416 89 12 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 90 1 + + ADP bibechana-46416 90 2 1 1 X bibechana-46416 90 3 ) ) PUNCT bibechana-46416 90 4 βˆ’ βˆ’ NOUN bibechana-46416 91 1 1 1 NUM bibechana-46416 91 2 2 2 NUM bibechana-46416 91 3 βˆ’ βˆ’ NUM bibechana-46416 91 4 𝑛 𝑛 NOUN bibechana-46416 91 5 ) ) PUNCT bibechana-46416 92 1 + + NUM bibechana-46416 92 2 π‘šπ‘‰0 π‘šπ‘‰0 ADP bibechana-46416 92 3 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 92 4 ( ( PUNCT bibechana-46416 92 5 √ √ NUM bibechana-46416 92 6 1 1 NUM bibechana-46416 92 7 4βˆ’ 4βˆ’ NUM bibechana-46416 92 8 𝑙 𝑙 X bibechana-46416 92 9 ( ( PUNCT bibechana-46416 92 10 𝑙 𝑙 PROPN bibechana-46416 92 11 + + NUM bibechana-46416 93 1 1 1 NUM bibechana-46416 93 2 ) ) PUNCT bibechana-46416 93 3 βˆ’ βˆ’ NOUN bibechana-46416 93 4 1 1 NUM bibechana-46416 93 5 2 2 NUM bibechana-46416 93 6 βˆ’ βˆ’ NUM bibechana-46416 93 7 𝑛 𝑛 NOUN bibechana-46416 93 8 ) ) PUNCT bibechana-46416 93 9 ) ) PUNCT bibechana-46416 93 10 2 2 NUM bibechana-46416 93 11 ( ( PUNCT bibechana-46416 93 12 8) 8) NUM bibechana-46416 93 13 this this DET bibechana-46416 93 14 equation equation NOUN bibechana-46416 93 15 is be AUX bibechana-46416 93 16 dependent dependent ADJ bibechana-46416 93 17 upon upon SCONJ bibechana-46416 93 18 the the DET bibechana-46416 93 19 quantum quantum ADJ bibechana-46416 93 20 number number NOUN bibechana-46416 93 21 and and CCONJ bibechana-46416 93 22 screening screen VERB bibechana-46416 93 23 parameters parameter NOUN bibechana-46416 93 24 . . PUNCT bibechana-46416 94 1 it it PRON bibechana-46416 94 2 is be AUX bibechana-46416 94 3 a a DET bibechana-46416 94 4 non non ADJ bibechana-46416 94 5 - - ADJ bibechana-46416 94 6 relativistic relativistic ADJ bibechana-46416 94 7 energy energy NOUN bibechana-46416 94 8 spectrum spectrum NOUN bibechana-46416 94 9 that that PRON bibechana-46416 94 10 was be AUX bibechana-46416 94 11 calculated calculate VERB bibechana-46416 94 12 using use VERB bibechana-46416 94 13 hp hp PROPN bibechana-46416 94 14 , , PUNCT bibechana-46416 94 15 which which PRON bibechana-46416 94 16 is be AUX bibechana-46416 94 17 short short ADJ bibechana-46416 94 18 - - PUNCT bibechana-46416 94 19 range range NOUN bibechana-46416 94 20 potential potential NOUN bibechana-46416 94 21 . . PUNCT bibechana-46416 95 1 table1 table1 NOUN bibechana-46416 95 2 : : PUNCT bibechana-46416 95 3 energy energy PROPN bibechana-46416 95 4 eigenvalue eigenvalue PROPN bibechana-46416 95 5 of of ADP bibechana-46416 95 6 q q NOUN bibechana-46416 95 7 - - PUNCT bibechana-46416 95 8 deformed deform VERB bibechana-46416 95 9 hp hp ADJ bibechana-46416 95 10 quantum quantum ADJ bibechana-46416 95 11 number number NOUN bibechana-46416 95 12 energy energy NOUN bibechana-46416 95 13 eigenvalue eigenvalue NOUN bibechana-46416 95 14 ( ( PUNCT bibechana-46416 95 15 𝑬𝒏𝒍 𝑬𝒏𝒍 PROPN bibechana-46416 95 16 ) ) PUNCT bibechana-46416 95 17 𝑛 𝑛 PART bibechana-46416 95 18 𝑙 𝑙 NOUN bibechana-46416 95 19 𝑉0 𝑉0 NOUN bibechana-46416 95 20 = = SYM bibechana-46416 95 21 1 1 NUM bibechana-46416 95 22 , , PUNCT bibechana-46416 95 23 𝛼 𝛼 NOUN bibechana-46416 95 24 = = NOUN bibechana-46416 95 25 1 1 NUM bibechana-46416 95 26 𝑉0 𝑉0 NOUN bibechana-46416 95 27 = = SYM bibechana-46416 95 28 1 1 NUM bibechana-46416 95 29 , , PUNCT bibechana-46416 95 30 𝛼 𝛼 NOUN bibechana-46416 95 31 = = SYM bibechana-46416 95 32 0.5 0.5 NUM bibechana-46416 95 33 𝑉0 𝑉0 NOUN bibechana-46416 95 34 = = SYM bibechana-46416 95 35 0.5 0.5 NUM bibechana-46416 95 36 , , PUNCT bibechana-46416 95 37 𝛼 𝛼 NOUN bibechana-46416 95 38 = = NOUN bibechana-46416 95 39 1 1 NUM bibechana-46416 95 40 𝑉0 𝑉0 NOUN bibechana-46416 95 41 = = SYM bibechana-46416 95 42 0.1 0.1 NUM bibechana-46416 95 43 , , PUNCT bibechana-46416 95 44 𝛼 𝛼 NOUN bibechana-46416 95 45 = = NOUN bibechana-46416 95 46 1 1 NUM bibechana-46416 95 47 𝑉0 𝑉0 NOUN bibechana-46416 95 48 = = SYM bibechana-46416 95 49 0.1 0.1 NUM bibechana-46416 95 50 , , PUNCT bibechana-46416 95 51 𝛼 𝛼 NOUN bibechana-46416 95 52 = = NOUN bibechana-46416 95 53 0.1 0.1 NUM bibechana-46416 95 54 1 1 NUM bibechana-46416 95 55 0 0 NUM bibechana-46416 95 56 2.20977 2.20977 NUM bibechana-46416 95 57 531 531 NUM bibechana-46416 95 58 -2.2942 -2.2942 NOUN bibechana-46416 95 59 1.511428 1.511428 NUM bibechana-46416 95 60 202 202 NUM bibechana-46416 95 61 1.047957 1.047957 NUM bibechana-46416 95 62 128 128 NUM bibechana-46416 95 63 -0.37392 -0.37392 NOUN bibechana-46416 95 64 1 1 NUM bibechana-46416 95 65 -3.909 -3.909 NOUN bibechana-46416 95 66 -2.0596 -2.0596 NOUN bibechana-46416 95 67 3.342473 3.342473 NUM bibechana-46416 95 68 165 165 NUM bibechana-46416 95 69 2.921198 2.921198 NUM bibechana-46416 95 70 927 927 NUM bibechana-46416 95 71 -0.21685 -0.21685 NOUN bibechana-46416 95 72 2 2 NUM bibechana-46416 95 73 0 0 NUM bibechana-46416 95 74 3.90895 3.90895 NUM bibechana-46416 95 75 5159 5159 NUM bibechana-46416 95 76 2.059648 2.059648 NUM bibechana-46416 95 77 762 762 NUM bibechana-46416 95 78 3.342473 3.342473 NUM bibechana-46416 95 79 165 165 NUM bibechana-46416 95 80 2.921198 2.921198 NUM bibechana-46416 95 81 927 927 NUM bibechana-46416 95 82 -0.21685 -0.21685 NOUN bibechana-46416 95 83 1 1 NUM bibechana-46416 95 84 6.73920 6.73920 NUM bibechana-46416 95 85 8248 8248 NUM bibechana-46416 95 86 2.599411 2.599411 NUM bibechana-46416 95 87 115 115 NUM bibechana-46416 95 88 6.206286 6.206286 NUM bibechana-46416 95 89 437 437 NUM bibechana-46416 95 90 5.795751 5.795751 NUM bibechana-46416 95 91 457 457 NUM bibechana-46416 95 92 -0.20085 -0.20085 NOUN bibechana-46416 95 93 2 2 NUM bibechana-46416 95 94 15.4626 15.4626 NUM bibechana-46416 95 95 1915 1915 NUM bibechana-46416 95 96 4.680554 4.680554 NUM bibechana-46416 95 97 734 734 NUM bibechana-46416 95 98 14.94963 14.94963 NUM bibechana-46416 95 99 916 916 NUM bibechana-46416 95 100 14.54548 14.54548 NUM bibechana-46416 95 101 557 557 NUM bibechana-46416 95 102 -0.26176 -0.26176 NOUN bibechana-46416 95 103 3 3 NUM bibechana-46416 95 104 0 0 NUM bibechana-46416 95 105 6.73920 6.73920 NUM bibechana-46416 95 106 8248 8248 NUM bibechana-46416 95 107 2.599411 2.599411 NUM bibechana-46416 95 108 115 115 NUM bibechana-46416 95 109 6.206286 6.206286 NUM bibechana-46416 95 110 437 437 NUM bibechana-46416 95 111 5.795751 5.795751 NUM bibechana-46416 95 112 457 457 NUM bibechana-46416 95 113 -0.20085 -0.20085 NOUN bibechana-46416 95 114 1 1 NUM bibechana-46416 95 115 10.5964 10.5964 NUM bibechana-46416 95 116 3495 3495 NUM bibechana-46416 95 117 3.497067 3.497067 NUM bibechana-46416 95 118 921 921 NUM bibechana-46416 95 119 10.07684 10.07684 NUM bibechana-46416 95 120 311 311 NUM bibechana-46416 95 121 9.670573 9.670573 NUM bibechana-46416 95 122 724 724 NUM bibechana-46416 95 123 -0.22183 -0.22183 NOUN bibechana-46416 95 124 2 2 NUM bibechana-46416 95 125 21.3326 21.3326 NUM bibechana-46416 95 126 1546 1546 NUM bibechana-46416 95 127 6.129289 6.129289 NUM bibechana-46416 95 128 967 967 NUM bibechana-46416 95 129 20.82338 20.82338 NUM bibechana-46416 95 130 824 824 NUM bibechana-46416 95 131 20.42043 20.42043 NUM bibechana-46416 95 132 553 553 NUM bibechana-46416 95 133 -0.31551 -0.31551 NOUN bibechana-46416 95 134 3 3 NUM bibechana-46416 95 135 44.9510 44.9510 NUM bibechana-46416 95 136 0139 0139 NUM bibechana-46416 95 137 12.00908 12.00908 NUM bibechana-46416 95 138 368 368 NUM bibechana-46416 95 139 44.44673 44.44673 NUM bibechana-46416 95 140 472 472 NUM bibechana-46416 95 141 44.04536 44.04536 NUM bibechana-46416 95 142 939 939 NUM bibechana-46416 95 143 -0.54514 -0.54514 NOUN bibechana-46416 95 144 4 4 NUM bibechana-46416 95 145 0 0 NUM bibechana-46416 95 146 15.4626 15.4626 NUM bibechana-46416 95 147 1915 1915 NUM bibechana-46416 96 1 3.497067 3.497067 NUM bibechana-46416 96 2 921 921 NUM bibechana-46416 96 3 10.07684 10.07684 NUM bibechana-46416 96 4 311 311 NUM bibechana-46416 96 5 9.670573 9.670573 NUM bibechana-46416 96 6 724 724 NUM bibechana-46416 96 7 -0.22183 -0.22183 NOUN bibechana-46416 96 8 1 1 NUM bibechana-46416 96 9 21.3326 21.3326 NUM bibechana-46416 96 10 1546 1546 NUM bibechana-46416 96 11 4.680554 4.680554 NUM bibechana-46416 96 12 734 734 NUM bibechana-46416 96 13 14.94963 14.94963 NUM bibechana-46416 96 14 916 916 NUM bibechana-46416 96 15 14.54548 14.54548 NUM bibechana-46416 96 16 557 557 NUM bibechana-46416 96 17 -0.26176 -0.26176 NOUN bibechana-46416 96 18 2 2 NUM bibechana-46416 96 19 36.0774 36.0774 NUM bibechana-46416 96 20 4104 4104 NUM bibechana-46416 96 21 7.835599 7.835599 NUM bibechana-46416 96 22 168 168 NUM bibechana-46416 96 23 27.69761 27.69761 NUM bibechana-46416 96 24 069 069 NUM bibechana-46416 96 25 27.29540 27.29540 NUM bibechana-46416 96 26 443 443 NUM bibechana-46416 96 27 -0.38115 -0.38115 NOUN bibechana-46416 96 28 3 3 NUM bibechana-46416 96 29 65.6991 65.6991 NUM bibechana-46416 96 30 7677 7677 NUM bibechana-46416 96 31 14.47365 14.47365 NUM bibechana-46416 96 32 847 847 NUM bibechana-46416 96 33 54.32147 54.32147 NUM bibechana-46416 96 34 377 377 NUM bibechana-46416 96 35 53.92035 53.92035 NUM bibechana-46416 96 36 895 895 NUM bibechana-46416 96 37 -0.64285 -0.64285 NOUN bibechana-46416 96 38 4 4 NUM bibechana-46416 96 39 119.197 119.197 NUM bibechana-46416 96 40 4276 4276 NUM bibechana-46416 96 41 26.83975 26.83975 NUM bibechana-46416 96 42 676 676 NUM bibechana-46416 96 43 103.8209 103.8209 NUM bibechana-46416 96 44 174 174 NUM bibechana-46416 96 45 103.4203 103.4203 NUM bibechana-46416 96 46 367 367 NUM bibechana-46416 96 47 -1.13562 -1.13562 NOUN bibechana-46416 96 48 5 5 NUM bibechana-46416 96 49 0 0 NUM bibechana-46416 96 50 15.4626 15.4626 NUM bibechana-46416 96 51 1915 1915 NUM bibechana-46416 96 52 4.680554 4.680554 NUM bibechana-46416 96 53 734 734 NUM bibechana-46416 96 54 14.94963 14.94963 NUM bibechana-46416 96 55 916 916 NUM bibechana-46416 96 56 14.54548 14.54548 NUM bibechana-46416 96 57 557 557 NUM bibechana-46416 96 58 -0.26176 -0.26176 NOUN bibechana-46416 96 59 karki karki PROPN bibechana-46416 96 60 et et PROPN bibechana-46416 96 61 al al PROPN bibechana-46416 96 62 . . PUNCT bibechana-46416 96 63 / / SYM bibechana-46416 96 64 bibechana bibechana PROPN bibechana-46416 96 65 19(1 19(1 NUM bibechana-46416 96 66 - - SYM bibechana-46416 96 67 2 2 NUM bibechana-46416 96 68 ) ) PUNCT bibechana-46416 96 69 ( ( PUNCT bibechana-46416 96 70 2022 2022 NUM bibechana-46416 96 71 ) ) PUNCT bibechana-46416 96 72 165 165 NUM bibechana-46416 96 73 - - SYM bibechana-46416 96 74 169 169 NUM bibechana-46416 96 75 168 168 NUM bibechana-46416 96 76 1 1 NUM bibechana-46416 96 77 21.3326 21.3326 NUM bibechana-46416 96 78 1546 1546 NUM bibechana-46416 96 79 6.129289 6.129289 NUM bibechana-46416 96 80 967 967 NUM bibechana-46416 96 81 20.82338 20.82338 NUM bibechana-46416 96 82 824 824 NUM bibechana-46416 96 83 20.42043 20.42043 NUM bibechana-46416 96 84 553 553 NUM bibechana-46416 96 85 -0.31551 -0.31551 NOUN bibechana-46416 96 86 2 2 NUM bibechana-46416 96 87 36.0774 36.0774 NUM bibechana-46416 96 88 4104 4104 NUM bibechana-46416 96 89 9.796092 9.796092 NUM bibechana-46416 96 90 271 271 NUM bibechana-46416 96 91 35.57209 35.57209 NUM bibechana-46416 96 92 463 463 NUM bibechana-46416 96 93 35.17038 35.17038 NUM bibechana-46416 96 94 379 379 NUM bibechana-46416 96 95 -0.45783 -0.45783 NOUN bibechana-46416 96 96 3 3 NUM bibechana-46416 96 97 65.6991 65.6991 NUM bibechana-46416 96 98 7677 7677 NUM bibechana-46416 96 99 17.18928 17.18928 NUM bibechana-46416 96 100 52 52 NUM bibechana-46416 96 101 65.19627 65.19627 NUM bibechana-46416 96 102 857 857 NUM bibechana-46416 96 103 64.79535 64.79535 NUM bibechana-46416 96 104 114 114 NUM bibechana-46416 96 105 -0.75082 -0.75082 NOUN bibechana-46416 96 106 4 4 NUM bibechana-46416 96 107 119.197 119.197 NUM bibechana-46416 96 108 4276 4276 NUM bibechana-46416 96 109 30.55728 30.55728 NUM bibechana-46416 96 110 87 87 NUM bibechana-46416 96 111 118.6958 118.6958 NUM bibechana-46416 96 112 413 413 NUM bibechana-46416 96 113 118.2953 118.2953 NUM bibechana-46416 96 114 337 337 NUM bibechana-46416 96 115 -1.28407 -1.28407 NOUN bibechana-46416 96 116 5 5 NUM bibechana-46416 96 117 208.571 208.571 NUM bibechana-46416 96 118 5169 5169 NUM bibechana-46416 96 119 52.89739 52.89739 NUM bibechana-46416 96 120 577 577 NUM bibechana-46416 96 121 208.0706 208.0706 NUM bibechana-46416 96 122 136 136 NUM bibechana-46416 96 123 207.6703 207.6703 NUM bibechana-46416 96 124 245 245 NUM bibechana-46416 96 125 -2.17691 -2.17691 PROPN bibechana-46416 96 126 2.1 2.1 NUM bibechana-46416 96 127 . . PUNCT bibechana-46416 97 1 thermodynamic thermodynamic ADJ bibechana-46416 97 2 properties property NOUN bibechana-46416 97 3 hp hp NOUN bibechana-46416 97 4 is be AUX bibechana-46416 97 5 also also ADV bibechana-46416 97 6 used use VERB bibechana-46416 97 7 to to PART bibechana-46416 97 8 explain explain VERB bibechana-46416 97 9 the the DET bibechana-46416 97 10 electronic electronic ADJ bibechana-46416 97 11 properties property NOUN bibechana-46416 97 12 of of ADP bibechana-46416 97 13 some some DET bibechana-46416 97 14 alkali alkali ADJ bibechana-46416 97 15 halides halide NOUN bibechana-46416 97 16 , , PUNCT bibechana-46416 97 17 study study VERB bibechana-46416 97 18 the the DET bibechana-46416 97 19 bound bound ADJ bibechana-46416 97 20 state state NOUN bibechana-46416 97 21 and and CCONJ bibechana-46416 97 22 scattering scatter VERB bibechana-46416 97 23 properties property NOUN bibechana-46416 97 24 , , PUNCT bibechana-46416 97 25 etc etc X bibechana-46416 97 26 . . X bibechana-46416 98 1 moreover moreover ADV bibechana-46416 98 2 , , PUNCT bibechana-46416 98 3 statistical statistical ADJ bibechana-46416 98 4 physics physics NOUN bibechana-46416 98 5 and and CCONJ bibechana-46416 98 6 quantum quantum ADJ bibechana-46416 98 7 statistical statistical ADJ bibechana-46416 98 8 mechanics mechanic NOUN bibechana-46416 98 9 help help VERB bibechana-46416 98 10 predict predict VERB bibechana-46416 98 11 , , PUNCT bibechana-46416 98 12 interpret interpret VERB bibechana-46416 98 13 , , PUNCT bibechana-46416 98 14 analyze analyze NOUN bibechana-46416 98 15 , , PUNCT bibechana-46416 98 16 etc etc X bibechana-46416 98 17 . . X bibechana-46416 98 18 , , PUNCT bibechana-46416 98 19 different different ADJ bibechana-46416 98 20 thermodynamic thermodynamic ADJ bibechana-46416 98 21 properties property NOUN bibechana-46416 98 22 such such ADJ bibechana-46416 98 23 as as ADP bibechana-46416 98 24 vibrational vibrational ADJ bibechana-46416 98 25 and and CCONJ bibechana-46416 98 26 rotational rotational ADJ bibechana-46416 98 27 energy energy NOUN bibechana-46416 98 28 levels level NOUN bibechana-46416 98 29 of of ADP bibechana-46416 98 30 various various ADJ bibechana-46416 98 31 molecules molecule NOUN bibechana-46416 99 1 [ [ X bibechana-46416 99 2 6 6 NUM bibechana-46416 99 3 ] ] PUNCT bibechana-46416 99 4 . . PUNCT bibechana-46416 100 1 thermodynamics thermodynamic NOUN bibechana-46416 100 2 properties property NOUN bibechana-46416 100 3 of of ADP bibechana-46416 100 4 hp hp PROPN bibechana-46416 100 5 are be AUX bibechana-46416 100 6 also also ADV bibechana-46416 100 7 studied study VERB bibechana-46416 100 8 for for ADP bibechana-46416 100 9 statistical statistical ADJ bibechana-46416 100 10 quantum quantum ADJ bibechana-46416 100 11 chromodynamics chromodynamic NOUN bibechana-46416 100 12 ( ( PUNCT bibechana-46416 100 13 qcd qcd PROPN bibechana-46416 100 14 ) ) PUNCT bibechana-46416 100 15 , , PUNCT bibechana-46416 100 16 nuclear nuclear ADJ bibechana-46416 100 17 matter matter NOUN bibechana-46416 100 18 , , PUNCT bibechana-46416 100 19 a a DET bibechana-46416 100 20 color color NOUN bibechana-46416 100 21 deconfined deconfine VERB bibechana-46416 100 22 partonic partonic ADJ bibechana-46416 100 23 phase phase NOUN bibechana-46416 100 24 , , PUNCT bibechana-46416 100 25 and and CCONJ bibechana-46416 100 26 the the DET bibechana-46416 100 27 quark quark ADJ bibechana-46416 100 28 - - PUNCT bibechana-46416 100 29 gluon gluon NOUN bibechana-46416 100 30 plasma plasma NOUN bibechana-46416 100 31 ( ( PUNCT bibechana-46416 100 32 qgp qgp NOUN bibechana-46416 100 33 ) ) PUNCT bibechana-46416 100 34 at at ADP bibechana-46416 100 35 sufficiently sufficiently ADV bibechana-46416 100 36 high high ADJ bibechana-46416 100 37 temperature temperature NOUN bibechana-46416 100 38 / / SYM bibechana-46416 100 39 density density NOUN bibechana-46416 100 40 [ [ X bibechana-46416 100 41 7 7 NUM bibechana-46416 100 42 ] ] PUNCT bibechana-46416 100 43 . . PUNCT bibechana-46416 101 1 now now ADV bibechana-46416 101 2 to to PART bibechana-46416 101 3 calculate calculate VERB bibechana-46416 101 4 the the DET bibechana-46416 101 5 thermodynamic thermodynamic ADJ bibechana-46416 101 6 properties property NOUN bibechana-46416 101 7 for for ADP bibechana-46416 101 8 hp hp NOUN bibechana-46416 101 9 , , PUNCT bibechana-46416 101 10 now now ADV bibechana-46416 101 11 we we PRON bibechana-46416 101 12 develop develop VERB bibechana-46416 101 13 ( ( PUNCT bibechana-46416 101 14 8) 8) NUM bibechana-46416 101 15 equation equation NOUN bibechana-46416 101 16 to to PART bibechana-46416 101 17 study study VERB bibechana-46416 101 18 the the DET bibechana-46416 101 19 thermodynamic thermodynamic ADJ bibechana-46416 101 20 properties property NOUN bibechana-46416 101 21 ; ; PUNCT bibechana-46416 101 22 we we PRON bibechana-46416 101 23 use use VERB bibechana-46416 101 24 the the DET bibechana-46416 101 25 vibrational vibrational ADJ bibechana-46416 101 26 partition partition NOUN bibechana-46416 101 27 function function NOUN bibechana-46416 101 28 for for ADP bibechana-46416 101 29 this this PRON bibechana-46416 101 30 we we PRON bibechana-46416 101 31 summarized summarize VERB bibechana-46416 101 32 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 101 33 as as ADP bibechana-46416 101 34 , , PUNCT bibechana-46416 101 35 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 101 36 = = PUNCT bibechana-46416 101 37 βˆ’ βˆ’ NOUN bibechana-46416 101 38 ℏ2𝛼2 ℏ2𝛼2 NOUN bibechana-46416 101 39 2π‘š 2π‘š NOUN bibechana-46416 101 40 ( ( PUNCT bibechana-46416 101 41 𝑃 𝑃 PROPN bibechana-46416 101 42 ( ( PUNCT bibechana-46416 101 43 𝜎 𝜎 NOUN bibechana-46416 101 44 + + CCONJ bibechana-46416 101 45 𝑛 𝑛 NOUN bibechana-46416 101 46 ) ) PUNCT bibechana-46416 101 47 βˆ’ βˆ’ PROPN bibechana-46416 102 1 ( ( PUNCT bibechana-46416 102 2 𝜎 𝜎 PROPN bibechana-46416 102 3 + + CCONJ bibechana-46416 102 4 𝑛 𝑛 NOUN bibechana-46416 102 5 ) ) PUNCT bibechana-46416 102 6 ) ) PUNCT bibechana-46416 102 7 2 2 NUM bibechana-46416 102 8 ( ( PUNCT bibechana-46416 102 9 9 9 NUM bibechana-46416 102 10 ) ) PUNCT bibechana-46416 102 11 here here ADV bibechana-46416 102 12 , , PUNCT bibechana-46416 102 13 βˆ’πœŽ βˆ’πœŽ PROPN bibechana-46416 102 14 = = PUNCT bibechana-46416 102 15 βˆ’ βˆ’ PROPN bibechana-46416 102 16 1 1 NUM bibechana-46416 102 17 2 2 NUM bibechana-46416 102 18 + + CCONJ bibechana-46416 102 19 √ √ NUM bibechana-46416 102 20 1 1 NUM bibechana-46416 102 21 4 4 NUM bibechana-46416 102 22 βˆ’ βˆ’ NOUN bibechana-46416 102 23 𝑙(𝑙 𝑙(𝑙 X bibechana-46416 103 1 + + ADP bibechana-46416 103 2 1 1 NUM bibechana-46416 103 3 ) ) PUNCT bibechana-46416 103 4 , , PUNCT bibechana-46416 103 5 𝑃 𝑃 NOUN bibechana-46416 103 6 = = PUNCT bibechana-46416 103 7 βˆ’ βˆ’ PROPN bibechana-46416 103 8 π‘šπ‘‰0 π‘šπ‘‰0 PROPN bibechana-46416 103 9 2ℏ2𝛼2 2ℏ2𝛼2 NUM bibechana-46416 103 10 , , PUNCT bibechana-46416 103 11 since since SCONJ bibechana-46416 103 12 vibrational vibrational ADJ bibechana-46416 103 13 partition partition NOUN bibechana-46416 103 14 function function NOUN bibechana-46416 103 15 is be AUX bibechana-46416 103 16 defined define VERB bibechana-46416 103 17 as as ADP bibechana-46416 103 18 𝑍𝑣𝑖𝑏(𝛽 𝑍𝑣𝑖𝑏(𝛽 X bibechana-46416 103 19 ) ) PUNCT bibechana-46416 103 20 = = PUNCT bibechana-46416 104 1 βˆ‘ βˆ‘ PUNCT bibechana-46416 104 2 π‘’βˆ’π›½πΈπ‘›π‘™ π‘’βˆ’π›½πΈπ‘›π‘™ PUNCT bibechana-46416 104 3 πœ‚ πœ‚ X bibechana-46416 104 4 𝑛=0 𝑛=0 PROPN bibechana-46416 104 5 , , PUNCT bibechana-46416 104 6 𝛽 𝛽 NOUN bibechana-46416 104 7 = = SYM bibechana-46416 104 8 1 1 NUM bibechana-46416 104 9 π‘˜π‘‡ π‘˜π‘‡ PROPN bibechana-46416 104 10 therefore therefore ADV bibechana-46416 104 11 , , PUNCT bibechana-46416 104 12 substituting substitute VERB bibechana-46416 104 13 the the DET bibechana-46416 104 14 value value NOUN bibechana-46416 104 15 of of ADP bibechana-46416 104 16 𝐸𝑛𝑙 𝐸𝑛𝑙 PROPN bibechana-46416 104 17 in in ADP bibechana-46416 104 18 𝑍𝑣𝑖𝑏 𝑍𝑣𝑖𝑏 PROPN bibechana-46416 104 19 hp hp NOUN bibechana-46416 104 20 with with ADP bibechana-46416 104 21 partition partition NOUN bibechana-46416 104 22 function function NOUN bibechana-46416 104 23 modified modify VERB bibechana-46416 104 24 as as ADP bibechana-46416 104 25 , , PUNCT bibechana-46416 104 26 𝑍𝑣𝑖𝑏(𝛽 𝑍𝑣𝑖𝑏(𝛽 NUM bibechana-46416 104 27 ) ) PUNCT bibechana-46416 104 28 = = PUNCT bibechana-46416 104 29 βˆ‘ βˆ‘ PUNCT bibechana-46416 104 30 𝑒 𝑒 PART bibechana-46416 104 31 βˆ’π›½[βˆ’ βˆ’π›½[βˆ’ NOUN bibechana-46416 104 32 ℏ2𝛼2 ℏ2𝛼2 NOUN bibechana-46416 104 33 2π‘š 2π‘š NOUN bibechana-46416 104 34 ( ( PUNCT bibechana-46416 104 35 𝑃 𝑃 NOUN bibechana-46416 104 36 ( ( PUNCT bibechana-46416 104 37 𝜎+𝑛 𝜎+𝑛 NUM bibechana-46416 104 38 ) ) PUNCT bibechana-46416 104 39 βˆ’(𝜎+𝑛 βˆ’(𝜎+𝑛 NOUN bibechana-46416 104 40 ) ) PUNCT bibechana-46416 104 41 ) ) PUNCT bibechana-46416 105 1 2 2 NUM bibechana-46416 105 2 ] ] SYM bibechana-46416 105 3 πœ‚ πœ‚ X bibechana-46416 105 4 𝑛=0 𝑛=0 PROPN bibechana-46416 105 5 ( ( PUNCT bibechana-46416 105 6 10 10 NUM bibechana-46416 105 7 ) ) PUNCT bibechana-46416 105 8 replacing replace VERB bibechana-46416 105 9 the the DET bibechana-46416 105 10 sum sum NOUN bibechana-46416 105 11 by by ADP bibechana-46416 105 12 an an DET bibechana-46416 105 13 integral integral ADJ bibechana-46416 105 14 in in ADP bibechana-46416 105 15 the the DET bibechana-46416 105 16 classical classical ADJ bibechana-46416 105 17 limit limit NOUN bibechana-46416 105 18 of of ADP bibechana-46416 105 19 equation equation NOUN bibechana-46416 105 20 ( ( PUNCT bibechana-46416 105 21 10 10 NUM bibechana-46416 105 22 ) ) PUNCT bibechana-46416 105 23 , , PUNCT bibechana-46416 105 24 we we PRON bibechana-46416 105 25 have have VERB bibechana-46416 105 26 𝑍𝑣𝑖𝑏(𝛽 𝑍𝑣𝑖𝑏(𝛽 NUM bibechana-46416 105 27 ) ) PUNCT bibechana-46416 105 28 = = SYM bibechana-46416 106 1 ∫ ∫ PROPN bibechana-46416 106 2 𝑒 𝑒 PROPN bibechana-46416 106 3 βˆ’π›½[βˆ’ βˆ’π›½[βˆ’ NOUN bibechana-46416 106 4 ℏ2𝛼2 ℏ2𝛼2 NOUN bibechana-46416 106 5 2π‘š 2π‘š NOUN bibechana-46416 106 6 ( ( PUNCT bibechana-46416 106 7 𝑃 𝑃 NOUN bibechana-46416 106 8 ( ( PUNCT bibechana-46416 106 9 𝜎+𝑛 𝜎+𝑛 NUM bibechana-46416 106 10 ) ) PUNCT bibechana-46416 106 11 βˆ’(𝜎+𝑛 βˆ’(𝜎+𝑛 NOUN bibechana-46416 106 12 ) ) PUNCT bibechana-46416 106 13 ) ) PUNCT bibechana-46416 106 14 2 2 NUM bibechana-46416 106 15 ] ] SYM bibechana-46416 106 16 πœ‚ πœ‚ X bibechana-46416 106 17 0 0 NUM bibechana-46416 106 18 𝑑𝑛 𝑑𝑛 X bibechana-46416 106 19 ( ( PUNCT bibechana-46416 106 20 11 11 NUM bibechana-46416 106 21 ) ) PUNCT bibechana-46416 106 22 supposing suppose VERB bibechana-46416 106 23 𝜎 𝜎 PROPN bibechana-46416 106 24 + + CCONJ bibechana-46416 106 25 𝑛 𝑛 PROPN bibechana-46416 106 26 = = SYM bibechana-46416 106 27 𝜌 𝜌 X bibechana-46416 106 28 , , PUNCT bibechana-46416 106 29 equation equation NOUN bibechana-46416 106 30 ( ( PUNCT bibechana-46416 106 31 becomescome becomescome NOUN bibechana-46416 106 32 [ [ X bibechana-46416 106 33 8 8 NUM bibechana-46416 106 34 ] ] SYM bibechana-46416 106 35 𝑍𝑣𝑖𝑏(𝛽 𝑍𝑣𝑖𝑏(𝛽 NUM bibechana-46416 106 36 ) ) PUNCT bibechana-46416 106 37 = = SYM bibechana-46416 106 38 ∫ ∫ PROPN bibechana-46416 106 39 𝑒 𝑒 PROPN bibechana-46416 106 40 ( ( PUNCT bibechana-46416 106 41 𝑏𝛽 𝑏𝛽 ADP bibechana-46416 106 42 𝜌2 𝜌2 PROPN bibechana-46416 106 43 + + NOUN bibechana-46416 106 44 π›½π‘ŽπœŒ2+𝑐𝛽 π›½π‘ŽπœŒ2+𝑐𝛽 NOUN bibechana-46416 106 45 ) ) PUNCT bibechana-46416 106 46 π‘‘πœŒ π‘‘πœŒ NOUN bibechana-46416 106 47 πœ‚+𝜎 πœ‚+𝜎 X bibechana-46416 106 48 𝜎 𝜎 X bibechana-46416 106 49 ( ( PUNCT bibechana-46416 106 50 12 12 NUM bibechana-46416 106 51 ) ) PUNCT bibechana-46416 106 52 here here ADV bibechana-46416 106 53 π‘Ž π‘Ž X bibechana-46416 106 54 = = SYM bibechana-46416 106 55 ℏ2𝛼2 ℏ2𝛼2 NOUN bibechana-46416 106 56 2π‘š 2π‘š NOUN bibechana-46416 106 57 , , PUNCT bibechana-46416 106 58 𝑏 𝑏 PROPN bibechana-46416 106 59 = = SYM bibechana-46416 106 60 ℏ2𝛼2𝑃2 ℏ2𝛼2𝑃2 NOUN bibechana-46416 106 61 2π‘š 2π‘š NOUN bibechana-46416 106 62 , , PUNCT bibechana-46416 106 63 𝑐 𝑐 NOUN bibechana-46416 106 64 = = PUNCT bibechana-46416 106 65 βˆ’ βˆ’ PROPN bibechana-46416 107 1 ℏ2𝛼2𝑃 ℏ2𝛼2𝑃 X bibechana-46416 107 2 π‘š π‘š NOUN bibechana-46416 107 3 , , PUNCT bibechana-46416 107 4 now now ADV bibechana-46416 107 5 equation equation NOUN bibechana-46416 107 6 ( ( PUNCT bibechana-46416 107 7 12 12 NUM bibechana-46416 107 8 ) ) PUNCT bibechana-46416 107 9 becomes become VERB bibechana-46416 107 10 𝑍𝑣𝑖𝑏(𝛽 𝑍𝑣𝑖𝑏(𝛽 NUM bibechana-46416 107 11 ) ) PUNCT bibechana-46416 107 12 = = SYM bibechana-46416 107 13 π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ NOUN bibechana-46416 107 14 ( ( PUNCT bibechana-46416 107 15 βˆ’ βˆ’ PROPN bibechana-46416 107 16 erf[Ξ³1 erf[Ξ³1 PROPN bibechana-46416 107 17 βˆ’ βˆ’ PROPN bibechana-46416 107 18 Ξ³2 Ξ³2 NOUN bibechana-46416 107 19 ] ] X bibechana-46416 108 1 + + CCONJ bibechana-46416 108 2 𝑒 𝑒 PROPN bibechana-46416 108 3 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 NUM bibechana-46416 108 4 + + CCONJ bibechana-46416 108 5 Ξ³2 Ξ³2 ADJ bibechana-46416 108 6 ] ] PUNCT bibechana-46416 108 7 βˆ’ βˆ’ PROPN bibechana-46416 109 1 erf[Ο‰1 erf[Ο‰1 PROPN bibechana-46416 109 2 + + CCONJ bibechana-46416 109 3 Ξ³2 Ξ³2 ADJ bibechana-46416 109 4 + + CCONJ bibechana-46416 109 5 Ο‰2 Ο‰2 NUM bibechana-46416 109 6 ] ] PUNCT bibechana-46416 109 7 ) ) PUNCT bibechana-46416 109 8 βˆ’ βˆ’ ADP bibechana-46416 109 9 ΞΎ ΞΎ X bibechana-46416 109 10 ) ) PUNCT bibechana-46416 109 11 4βˆšβˆ’π‘Žπ›½ 4βˆšβˆ’π‘Žπ›½ NOUN bibechana-46416 109 12 ( ( PUNCT bibechana-46416 109 13 13 13 NUM bibechana-46416 109 14 ) ) PUNCT bibechana-46416 109 15 where where SCONJ bibechana-46416 109 16 Ξ³1 Ξ³1 NOUN bibechana-46416 109 17 = = PROPN bibechana-46416 109 18 βˆšβˆ’π‘π›½ βˆšβˆ’π‘π›½ X bibechana-46416 109 19 𝜎 𝜎 X bibechana-46416 109 20 , , PUNCT bibechana-46416 109 21 Ξ³2 Ξ³2 NOUN bibechana-46416 109 22 = = PUNCT bibechana-46416 109 23 βˆšβˆ’π‘Žπ›½πœŽ,Ο‰1 βˆšβˆ’π‘Žπ›½πœŽ,Ο‰1 NOUN bibechana-46416 109 24 = = SYM bibechana-46416 109 25 βˆšβˆ’π‘Žπ›½πœ‚ βˆšβˆ’π‘Žπ›½πœ‚ NUM bibechana-46416 109 26 , , PUNCT bibechana-46416 109 27 Ο‰2 Ο‰2 NOUN bibechana-46416 109 28 = = SYM bibechana-46416 110 1 βˆšβˆ’π‘π›½ βˆšβˆ’π‘π›½ PROPN bibechana-46416 110 2 πœ‚+𝜎 πœ‚+𝜎 X bibechana-46416 110 3 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN bibechana-46416 110 4 ΞΎ ΞΎ PROPN bibechana-46416 110 5 = = SYM bibechana-46416 110 6 erf erf PROPN bibechana-46416 110 7 [ [ X bibechana-46416 110 8 Ο‰1 Ο‰1 PROPN bibechana-46416 110 9 + + CCONJ bibechana-46416 110 10 Ξ³2 Ξ³2 ADJ bibechana-46416 110 11 βˆ’ βˆ’ PROPN bibechana-46416 110 12 Ο‰2 Ο‰2 PROPN bibechana-46416 110 13 ] ] PUNCT bibechana-46416 110 14 and and CCONJ bibechana-46416 110 15 the the DET bibechana-46416 110 16 error error NOUN bibechana-46416 110 17 function function NOUN bibechana-46416 110 18 well well ADV bibechana-46416 110 19 - - PUNCT bibechana-46416 110 20 defined define VERB bibechana-46416 110 21 as as ADP bibechana-46416 110 22 erf(𝑍 erf(𝑍 NOUN bibechana-46416 110 23 ) ) PUNCT bibechana-46416 110 24 = = SYM bibechana-46416 110 25 2 2 NUM bibechana-46416 110 26 βˆšπœ‹ βˆšπœ‹ NUM bibechana-46416 110 27 ∫ ∫ PROPN bibechana-46416 110 28 𝑒𝑑 𝑒𝑑 PROPN bibechana-46416 110 29 2 2 NUM bibechana-46416 110 30 𝑑𝑑 𝑑𝑑 ADP bibechana-46416 110 31 𝑧 𝑧 SYM bibechana-46416 110 32 0 0 NUM bibechana-46416 110 33 equation equation NOUN bibechana-46416 110 34 ( ( PUNCT bibechana-46416 110 35 13 13 NUM bibechana-46416 110 36 ) ) PUNCT bibechana-46416 110 37 plays play VERB bibechana-46416 110 38 an an DET bibechana-46416 110 39 integral integral ADJ bibechana-46416 110 40 equation equation NOUN bibechana-46416 110 41 used use VERB bibechana-46416 110 42 to to PART bibechana-46416 110 43 describe describe VERB bibechana-46416 110 44 the the DET bibechana-46416 110 45 thermodynamic thermodynamic ADJ bibechana-46416 110 46 properties property NOUN bibechana-46416 110 47 of of ADP bibechana-46416 110 48 q q ADV bibechana-46416 110 49 - - PUNCT bibechana-46416 110 50 deformed deform VERB bibechana-46416 110 51 hp hp NOUN bibechana-46416 110 52 . . PUNCT bibechana-46416 111 1 this this DET bibechana-46416 111 2 equation equation NOUN bibechana-46416 111 3 described describe VERB bibechana-46416 111 4 vibrational vibrational ADJ bibechana-46416 111 5 mean mean NOUN bibechana-46416 111 6 and and CCONJ bibechana-46416 111 7 free free ADJ bibechana-46416 111 8 energy energy NOUN bibechana-46416 111 9 , , PUNCT bibechana-46416 111 10 vibrational vibrational ADJ bibechana-46416 111 11 entropy entropy NOUN bibechana-46416 111 12 , , PUNCT bibechana-46416 111 13 and and CCONJ bibechana-46416 111 14 specific specific ADJ bibechana-46416 111 15 heat heat NOUN bibechana-46416 111 16 capacity capacity NOUN bibechana-46416 111 17 . . PUNCT bibechana-46416 112 1 the the DET bibechana-46416 112 2 integrals integral NOUN bibechana-46416 112 3 error error NOUN bibechana-46416 112 4 function function NOUN bibechana-46416 112 5 erf erf NOUN bibechana-46416 112 6 ( ( PUNCT bibechana-46416 112 7 𝑍 𝑍 PROPN bibechana-46416 112 8 ) ) PUNCT bibechana-46416 112 9 has have VERB bibechana-46416 112 10 essential essential ADJ bibechana-46416 112 11 applications application NOUN bibechana-46416 112 12 in in ADP bibechana-46416 112 13 atomic atomic ADJ bibechana-46416 112 14 physics physics PROPN bibechana-46416 112 15 , , PUNCT bibechana-46416 112 16 astrophysics astrophysic NOUN bibechana-46416 112 17 , , PUNCT bibechana-46416 112 18 statistical statistical ADJ bibechana-46416 112 19 analysis analysis NOUN bibechana-46416 112 20 , , PUNCT bibechana-46416 112 21 etc etc X bibechana-46416 112 22 . . X bibechana-46416 113 1 [ [ X bibechana-46416 113 2 9 9 NUM bibechana-46416 113 3 ] ] SYM bibechana-46416 113 4 3 3 NUM bibechana-46416 113 5 . . NOUN bibechana-46416 113 6 results result NOUN bibechana-46416 113 7 and and CCONJ bibechana-46416 113 8 discussion discussion NOUN bibechana-46416 113 9 2.2 2.2 NUM bibechana-46416 113 10 . . PUNCT bibechana-46416 114 1 energy energy NOUN bibechana-46416 114 2 eigenvalue eigenvalue PROPN bibechana-46416 114 3 of of ADP bibechana-46416 114 4 q q NOUN bibechana-46416 114 5 - - PUNCT bibechana-46416 114 6 deformed deform VERB bibechana-46416 114 7 hp hp NOUN bibechana-46416 114 8 the the DET bibechana-46416 114 9 energy energy NOUN bibechana-46416 114 10 eigenvalue eigenvalue NOUN bibechana-46416 114 11 is be AUX bibechana-46416 114 12 represented represent VERB bibechana-46416 114 13 in in ADP bibechana-46416 114 14 atom atom NOUN bibechana-46416 114 15 unit unit NOUN bibechana-46416 114 16 with with ADP bibechana-46416 114 17 π‘š π‘š PROPN bibechana-46416 114 18 = = SYM bibechana-46416 114 19 ℏ ℏ PROPN bibechana-46416 114 20 = = SYM bibechana-46416 114 21 1 1 NUM bibechana-46416 114 22 , , PUNCT bibechana-46416 114 23 at at ADP bibechana-46416 114 24 𝑉0 𝑉0 NOUN bibechana-46416 114 25 = = SYM bibechana-46416 114 26 0.5 0.5 NUM bibechana-46416 114 27 , , PUNCT bibechana-46416 114 28 1 1 NUM bibechana-46416 114 29 and and CCONJ bibechana-46416 114 30 𝛼 𝛼 X bibechana-46416 114 31 = = SYM bibechana-46416 114 32 0.5 0.5 NUM bibechana-46416 114 33 , , PUNCT bibechana-46416 114 34 1 1 NUM bibechana-46416 114 35 . . PUNCT bibechana-46416 115 1 the the DET bibechana-46416 115 2 energy energy NOUN bibechana-46416 115 3 eigenvalue eigenvalue PROPN bibechana-46416 115 4 is be AUX bibechana-46416 115 5 developed develop VERB bibechana-46416 115 6 of of ADP bibechana-46416 115 7 q q NOUN bibechana-46416 115 8 - - PUNCT bibechana-46416 115 9 deformed deform VERB bibechana-46416 115 10 hp hp NOUN bibechana-46416 115 11 . . PUNCT bibechana-46416 116 1 it it PRON bibechana-46416 116 2 is be AUX bibechana-46416 116 3 beneficial beneficial ADJ bibechana-46416 116 4 to to PART bibechana-46416 116 5 calculate calculate VERB bibechana-46416 116 6 the the DET bibechana-46416 116 7 thermodynamic thermodynamic ADJ bibechana-46416 116 8 properties property NOUN bibechana-46416 116 9 of of ADP bibechana-46416 116 10 physics physics NOUN bibechana-46416 116 11 fields field NOUN bibechana-46416 116 12 like like ADP bibechana-46416 116 13 quantum quantum ADJ bibechana-46416 116 14 chromodynamics chromodynamic NOUN bibechana-46416 116 15 , , PUNCT bibechana-46416 116 16 meson meson NOUN bibechana-46416 116 17 - - PUNCT bibechana-46416 116 18 meson meson NOUN bibechana-46416 116 19 interaction interaction NOUN bibechana-46416 116 20 , , PUNCT bibechana-46416 116 21 nuclear nuclear ADJ bibechana-46416 116 22 matter matter NOUN bibechana-46416 116 23 color color NOUN bibechana-46416 116 24 chromodynamics chromodynamic NOUN bibechana-46416 116 25 , , PUNCT bibechana-46416 116 26 etc etc X bibechana-46416 116 27 . . X bibechana-46416 117 1 the the DET bibechana-46416 117 2 nature nature NOUN bibechana-46416 117 3 of of ADP bibechana-46416 117 4 energy energy NOUN bibechana-46416 117 5 eigenvalue eigenvalue NOUN bibechana-46416 117 6 with with ADP bibechana-46416 117 7 quantum quantum ADJ bibechana-46416 117 8 number number NOUN bibechana-46416 117 9 is be AUX bibechana-46416 117 10 shown show VERB bibechana-46416 117 11 in in ADP bibechana-46416 117 12 figure figure NOUN bibechana-46416 117 13 1 1 NUM bibechana-46416 117 14 , , PUNCT bibechana-46416 117 15 which which PRON bibechana-46416 117 16 shows show VERB bibechana-46416 117 17 that that SCONJ bibechana-46416 117 18 with with ADP bibechana-46416 117 19 an an DET bibechana-46416 117 20 increased increase VERB bibechana-46416 117 21 quantum quantum NOUN bibechana-46416 117 22 number number NOUN bibechana-46416 117 23 the the DET bibechana-46416 117 24 electron electron NOUN bibechana-46416 117 25 bounded bound VERB bibechana-46416 117 26 energy energy NOUN bibechana-46416 117 27 decreases decrease NOUN bibechana-46416 117 28 which which PRON bibechana-46416 117 29 means mean VERB bibechana-46416 117 30 the the DET bibechana-46416 117 31 electron electron NOUN bibechana-46416 117 32 goes goes AUX bibechana-46416 117 33 loosely loosely ADV bibechana-46416 117 34 bounded bound VERB bibechana-46416 117 35 with with ADP bibechana-46416 117 36 the the DET bibechana-46416 117 37 nucleus nucleus NOUN bibechana-46416 117 38 in in ADP bibechana-46416 117 39 an an DET bibechana-46416 117 40 atom atom NOUN bibechana-46416 117 41 . . PUNCT bibechana-46416 118 1 figure figure NOUN bibechana-46416 118 2 1 1 NUM bibechana-46416 118 3 : : PUNCT bibechana-46416 118 4 energy energy NOUN bibechana-46416 118 5 eigenvalue eigenvalue NOUN bibechana-46416 118 6 of of ADP bibechana-46416 118 7 q q NOUN bibechana-46416 118 8 - - PUNCT bibechana-46416 118 9 deformed deform VERB bibechana-46416 118 10 hulthen hulthen NOUN bibechana-46416 118 11 potential potential ADJ bibechana-46416 118 12 2.3 2.3 NUM bibechana-46416 118 13 . . PUNCT bibechana-46416 119 1 thermodynamic thermodynamic ADJ bibechana-46416 119 2 properties property NOUN bibechana-46416 119 3 of of ADP bibechana-46416 119 4 q q ADV bibechana-46416 119 5 - - PUNCT bibechana-46416 119 6 deformed deform VERB bibechana-46416 119 7 hp hp ADJ bibechana-46416 119 8 2.3.1 2.3.1 NUM bibechana-46416 119 9 . . PUNCT bibechana-46416 120 1 vibrational vibrational ADJ bibechana-46416 120 2 mean mean VERB bibechana-46416 120 3 energy energy NOUN bibechana-46416 120 4 of of ADP bibechana-46416 120 5 q q ADV bibechana-46416 120 6 - - PUNCT bibechana-46416 120 7 deformed deform VERB bibechana-46416 120 8 hp hp NOUN bibechana-46416 120 9 ( ( PUNCT bibechana-46416 120 10 vmeqhp vmeqhp NOUN bibechana-46416 120 11 ) ) PUNCT bibechana-46416 120 12 the the DET bibechana-46416 120 13 mean mean ADJ bibechana-46416 120 14 vibrational vibrational ADJ bibechana-46416 120 15 energy energy NOUN bibechana-46416 120 16 for for ADP bibechana-46416 120 17 the the DET bibechana-46416 120 18 hp hp PROPN bibechana-46416 120 19 model model NOUN bibechana-46416 120 20 is be AUX bibechana-46416 120 21 obtained obtain VERB bibechana-46416 120 22 as as ADP bibechana-46416 120 23 , , PUNCT bibechana-46416 120 24 π‘ˆ(𝛽 π‘ˆ(𝛽 PROPN bibechana-46416 120 25 ) ) PUNCT bibechana-46416 121 1 = = SYM bibechana-46416 121 2 πœ• πœ• PROPN bibechana-46416 121 3 πœ•π›½ πœ•π›½ PROPN bibechana-46416 121 4 ( ( PUNCT bibechana-46416 121 5 𝑙𝑛𝑍𝑣𝑖𝑏(𝛽 𝑙𝑛𝑍𝑣𝑖𝑏(𝛽 NOUN bibechana-46416 121 6 ) ) PUNCT bibechana-46416 121 7 ) ) PUNCT bibechana-46416 122 1 π‘ˆ(𝛽 π‘ˆ(𝛽 X bibechana-46416 122 2 ) ) PUNCT bibechana-46416 122 3 = = SYM bibechana-46416 123 1 πœ• πœ• PROPN bibechana-46416 123 2 πœ•π›½ πœ•π›½ VERB bibechana-46416 123 3 𝑙𝑛 𝑙𝑛 NOUN bibechana-46416 123 4 ( ( PUNCT bibechana-46416 123 5 π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ X bibechana-46416 123 6 ( ( PUNCT bibechana-46416 123 7 βˆ’erf[Ξ³1βˆ’Ξ³2]+𝑒 βˆ’erf[Ξ³1βˆ’Ξ³2]+𝑒 NOUN bibechana-46416 123 8 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1+Ξ³2]βˆ’erf[Ο‰1+Ξ³2+Ο‰2])βˆ’ΞΎ 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1+Ξ³2]βˆ’erf[Ο‰1+Ξ³2+Ο‰2])βˆ’ΞΎ NUM bibechana-46416 123 9 ) ) PUNCT bibechana-46416 123 10 4βˆšβˆ’π‘Žπ›½ 4βˆšβˆ’π‘Žπ›½ NOUN bibechana-46416 123 11 ) ) PUNCT bibechana-46416 123 12 by by ADP bibechana-46416 123 13 solving solve VERB bibechana-46416 123 14 this this DET bibechana-46416 123 15 equation equation NOUN bibechana-46416 123 16 , , PUNCT bibechana-46416 123 17 we we PRON bibechana-46416 123 18 get get VERB bibechana-46416 123 19 , , PUNCT bibechana-46416 123 20 π‘ˆ(𝛽 π‘ˆ(𝛽 PROPN bibechana-46416 123 21 ) ) PUNCT bibechana-46416 123 22 = = PUNCT bibechana-46416 124 1 𝑑(ln 𝑑(ln X bibechana-46416 124 2 { { PUNCT bibechana-46416 124 3 ( ( PUNCT bibechana-46416 124 4 π‘’π‘Ÿπ‘“[𝛀2βˆ’π›€2 π‘’π‘Ÿπ‘“[𝛀2βˆ’π›€2 PROPN bibechana-46416 124 5 ] ] NOUN bibechana-46416 124 6 ) ) PUNCT bibechana-46416 124 7 } } PUNCT bibechana-46416 124 8 ) ) PUNCT bibechana-46416 125 1 𝑑𝛽 𝑑𝛽 VERB bibechana-46416 126 1 + + CCONJ bibechana-46416 126 2 𝑑 𝑑 PROPN bibechana-46416 126 3 ln{erf[Ξ³1+Ξ³2 ln{erf[Ξ³1+Ξ³2 PROPN bibechana-46416 126 4 ] ] PUNCT bibechana-46416 126 5 } } PUNCT bibechana-46416 126 6 𝑑𝛽 𝑑𝛽 ADP bibechana-46416 126 7 βˆ’ βˆ’ PROPN bibechana-46416 126 8 𝑑 𝑑 PROPN bibechana-46416 126 9 ln{erf[Ο‰1+Ξ³2+Ο‰2 ln{erf[Ο‰1+Ξ³2+Ο‰2 PROPN bibechana-46416 126 10 ] ] X bibechana-46416 126 11 } } PUNCT bibechana-46416 126 12 𝑑𝛽 𝑑𝛽 INTJ bibechana-46416 126 13 ( ( PUNCT bibechana-46416 126 14 14 14 NUM bibechana-46416 126 15 ) ) PUNCT bibechana-46416 126 16 2.3.2 2.3.2 NUM bibechana-46416 126 17 . . PUNCT bibechana-46416 127 1 vibrational vibrational ADJ bibechana-46416 127 2 mean mean VERB bibechana-46416 127 3 free free ADJ bibechana-46416 127 4 energy energy NOUN bibechana-46416 127 5 of of ADP bibechana-46416 127 6 q q ADV bibechana-46416 127 7 - - PUNCT bibechana-46416 127 8 deformed deform VERB bibechana-46416 127 9 hp hp NOUN bibechana-46416 127 10 ( ( PUNCT bibechana-46416 127 11 vmefqhp vmefqhp NOUN bibechana-46416 127 12 ) ) PUNCT bibechana-46416 127 13 the the DET bibechana-46416 127 14 vibrational vibrational ADJ bibechana-46416 127 15 mean mean VERB bibechana-46416 127 16 free free ADJ bibechana-46416 127 17 energy energy NOUN bibechana-46416 127 18 is be AUX bibechana-46416 127 19 obtained obtain VERB bibechana-46416 127 20 as as ADP bibechana-46416 127 21 𝐹(𝛽 𝐹(𝛽 NOUN bibechana-46416 127 22 ) ) PUNCT bibechana-46416 127 23 = = SYM bibechana-46416 127 24 βˆ’π‘˜π‘‡π‘™π‘›(𝑍𝑣𝑖𝑏(𝛽 βˆ’π‘˜π‘‡π‘™π‘›(𝑍𝑣𝑖𝑏(𝛽 NOUN bibechana-46416 127 25 ) ) PUNCT bibechana-46416 127 26 ) ) PUNCT bibechana-46416 128 1 𝐹(𝛽 𝐹(𝛽 X bibechana-46416 128 2 ) ) PUNCT bibechana-46416 128 3 = = SYM bibechana-46416 128 4 βˆ’π‘˜π‘‡π‘™π‘› βˆ’π‘˜π‘‡π‘™π‘› NOUN bibechana-46416 128 5 ( ( PUNCT bibechana-46416 128 6 π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ NOUN bibechana-46416 128 7 ( ( PUNCT bibechana-46416 128 8 βˆ’ βˆ’ PROPN bibechana-46416 128 9 erf[Ξ³1 erf[Ξ³1 PROPN bibechana-46416 128 10 βˆ’ βˆ’ PROPN bibechana-46416 128 11 Ξ³2 Ξ³2 NOUN bibechana-46416 128 12 ] ] X bibechana-46416 129 1 + + CCONJ bibechana-46416 129 2 𝑒 𝑒 PROPN bibechana-46416 129 3 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 NUM bibechana-46416 129 4 + + CCONJ bibechana-46416 129 5 Ξ³2 Ξ³2 ADJ bibechana-46416 129 6 ] ] PUNCT bibechana-46416 129 7 βˆ’ βˆ’ PROPN bibechana-46416 130 1 erf[Ο‰1 erf[Ο‰1 PROPN bibechana-46416 130 2 + + CCONJ bibechana-46416 130 3 Ξ³2 Ξ³2 ADJ bibechana-46416 130 4 + + CCONJ bibechana-46416 130 5 Ο‰2 Ο‰2 NUM bibechana-46416 130 6 ] ] PUNCT bibechana-46416 130 7 ) ) PUNCT bibechana-46416 130 8 βˆ’ βˆ’ ADP bibechana-46416 130 9 ΞΎ ΞΎ X bibechana-46416 130 10 ) ) PUNCT bibechana-46416 130 11 4βˆšβˆ’π‘Žπ›½ 4βˆšβˆ’π‘Žπ›½ NOUN bibechana-46416 130 12 ) ) PUNCT bibechana-46416 130 13 𝐹(𝛽 𝐹(𝛽 X bibechana-46416 130 14 ) ) PUNCT bibechana-46416 130 15 = = PUNCT bibechana-46416 130 16 βˆ’π‘˜π‘‡[ln βˆ’π‘˜π‘‡[ln X bibechana-46416 130 17 { { PUNCT bibechana-46416 130 18 ( ( PUNCT bibechana-46416 130 19 π‘’π‘Ÿπ‘“[𝛀2 π‘’π‘Ÿπ‘“[𝛀2 PROPN bibechana-46416 130 20 βˆ’ βˆ’ PROPN bibechana-46416 130 21 𝛀2 𝛀2 PROPN bibechana-46416 130 22 ] ] X bibechana-46416 130 23 ) ) PUNCT bibechana-46416 130 24 } } PUNCT bibechana-46416 131 1 + + CCONJ bibechana-46416 131 2 ln{erf[Ξ³1 ln{erf[Ξ³1 X bibechana-46416 131 3 + + X bibechana-46416 131 4 Ξ³2 Ξ³2 ADJ bibechana-46416 131 5 ] ] X bibechana-46416 131 6 } } PUNCT bibechana-46416 131 7 βˆ’ βˆ’ ADP bibechana-46416 132 1 ln{erf[Ο‰1 ln{erf[Ο‰1 ADV bibechana-46416 132 2 + + CCONJ bibechana-46416 132 3 Ξ³2 Ξ³2 ADJ bibechana-46416 132 4 + + CCONJ bibechana-46416 132 5 Ο‰2 Ο‰2 ADJ bibechana-46416 132 6 ] ] X bibechana-46416 132 7 } } PUNCT bibechana-46416 132 8 + + CCONJ bibechana-46416 132 9 ln{ΞΎ ln{ΞΎ NOUN bibechana-46416 132 10 } } PUNCT bibechana-46416 132 11 ] ] PUNCT bibechana-46416 132 12 ( ( PUNCT bibechana-46416 132 13 15 15 X bibechana-46416 132 14 ) ) PUNCT bibechana-46416 132 15 karki karki NOUN bibechana-46416 132 16 et et PROPN bibechana-46416 132 17 al al PROPN bibechana-46416 132 18 . . PUNCT bibechana-46416 132 19 / / SYM bibechana-46416 132 20 bibechana bibechana PROPN bibechana-46416 132 21 19(1 19(1 NUM bibechana-46416 132 22 - - SYM bibechana-46416 132 23 2 2 NUM bibechana-46416 132 24 ) ) PUNCT bibechana-46416 132 25 ( ( PUNCT bibechana-46416 132 26 2022 2022 NUM bibechana-46416 132 27 ) ) PUNCT bibechana-46416 132 28 165 165 NUM bibechana-46416 132 29 - - SYM bibechana-46416 132 30 169 169 NUM bibechana-46416 132 31 169 169 NUM bibechana-46416 132 32 2.3.3 2.3.3 NUM bibechana-46416 132 33 . . PUNCT bibechana-46416 133 1 vibrational vibrational ADJ bibechana-46416 133 2 specific specific ADJ bibechana-46416 133 3 heat heat NOUN bibechana-46416 133 4 capacity capacity NOUN bibechana-46416 133 5 of of ADP bibechana-46416 133 6 q q ADV bibechana-46416 133 7 - - PUNCT bibechana-46416 133 8 deformed deform VERB bibechana-46416 133 9 hp hp NOUN bibechana-46416 133 10 ( ( PUNCT bibechana-46416 133 11 vshcqhp vshcqhp PROPN bibechana-46416 133 12 ) ) PUNCT bibechana-46416 133 13 the the DET bibechana-46416 133 14 vibrational vibrational ADJ bibechana-46416 133 15 specific specific ADJ bibechana-46416 133 16 heat heat NOUN bibechana-46416 133 17 capacity capacity NOUN bibechana-46416 133 18 ( ( PUNCT bibechana-46416 133 19 cs cs X bibechana-46416 133 20 ) ) PUNCT bibechana-46416 133 21 is be AUX bibechana-46416 133 22 given give VERB bibechana-46416 133 23 as as ADP bibechana-46416 133 24 𝐢𝑠(𝛽 𝐢𝑠(𝛽 NOUN bibechana-46416 133 25 ) ) PUNCT bibechana-46416 133 26 = = SYM bibechana-46416 134 1 π‘˜π›½ π‘˜π›½ NUM bibechana-46416 134 2 2 2 NUM bibechana-46416 134 3 πœ•2 πœ•2 NOUN bibechana-46416 134 4 πœ•π›½2 πœ•π›½2 PROPN bibechana-46416 134 5 ( ( PUNCT bibechana-46416 134 6 𝑙𝑛(𝑍𝑣𝑖𝑏(𝛽 𝑙𝑛(𝑍𝑣𝑖𝑏(𝛽 PROPN bibechana-46416 134 7 ) ) PUNCT bibechana-46416 134 8 ) ) PUNCT bibechana-46416 134 9 ) ) PUNCT bibechana-46416 135 1 𝐢𝑠(𝛽 𝐢𝑠(𝛽 PROPN bibechana-46416 135 2 ) ) PUNCT bibechana-46416 136 1 = = SYM bibechana-46416 137 1 π‘˜π›½2 π‘˜π›½2 NOUN bibechana-46416 137 2 πœ•2 πœ•2 PUNCT bibechana-46416 138 1 πœ•π›½2 πœ•π›½2 PROPN bibechana-46416 138 2 𝑙𝑛 𝑙𝑛 NOUN bibechana-46416 138 3 ( ( PUNCT bibechana-46416 138 4 π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ X bibechana-46416 138 5 ( ( PUNCT bibechana-46416 138 6 βˆ’erf[Ξ³1 βˆ’erf[Ξ³1 X bibechana-46416 138 7 βˆ’ βˆ’ PROPN bibechana-46416 138 8 Ξ³2 Ξ³2 NOUN bibechana-46416 138 9 ] ] X bibechana-46416 139 1 + + CCONJ bibechana-46416 139 2 𝑒 𝑒 PROPN bibechana-46416 139 3 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 NUM bibechana-46416 139 4 + + CCONJ bibechana-46416 139 5 Ξ³2 Ξ³2 ADJ bibechana-46416 139 6 ] ] PUNCT bibechana-46416 139 7 βˆ’ βˆ’ PROPN bibechana-46416 140 1 erf[Ο‰1 erf[Ο‰1 PROPN bibechana-46416 140 2 + + CCONJ bibechana-46416 140 3 Ξ³2 Ξ³2 PROPN bibechana-46416 140 4 + + ADJ bibechana-46416 140 5 Ο‰2 Ο‰2 ADJ bibechana-46416 140 6 ] ] PUNCT bibechana-46416 140 7 ) ) PUNCT bibechana-46416 140 8 βˆ’ βˆ’ ADP bibechana-46416 140 9 ΞΎ ΞΎ X bibechana-46416 140 10 ) ) PUNCT bibechana-46416 140 11 4βˆšβˆ’π‘Žπ›½ 4βˆšβˆ’π‘Žπ›½ NOUN bibechana-46416 140 12 ) ) PUNCT bibechana-46416 140 13 𝐢𝑠(𝛽 𝐢𝑠(𝛽 PROPN bibechana-46416 140 14 ) ) PUNCT bibechana-46416 140 15 = = SYM bibechana-46416 141 1 π‘˜π›½ π‘˜π›½ NUM bibechana-46416 141 2 2 2 NUM bibechana-46416 141 3 πœ•2 πœ•2 NOUN bibechana-46416 141 4 πœ•π›½2 πœ•π›½2 X bibechana-46416 141 5 ( ( PUNCT bibechana-46416 141 6 [ [ X bibechana-46416 141 7 ln ln X bibechana-46416 141 8 { { PUNCT bibechana-46416 141 9 ( ( PUNCT bibechana-46416 141 10 π‘’π‘Ÿπ‘“[𝛀2 π‘’π‘Ÿπ‘“[𝛀2 PROPN bibechana-46416 141 11 βˆ’ βˆ’ PROPN bibechana-46416 141 12 𝛀2 𝛀2 PROPN bibechana-46416 141 13 ] ] X bibechana-46416 141 14 ) ) PUNCT bibechana-46416 141 15 } } PUNCT bibechana-46416 142 1 + + CCONJ bibechana-46416 142 2 ln{erf[Ξ³1 ln{erf[Ξ³1 X bibechana-46416 142 3 + + X bibechana-46416 142 4 Ξ³2 Ξ³2 ADJ bibechana-46416 142 5 ] ] X bibechana-46416 142 6 } } PUNCT bibechana-46416 142 7 βˆ’ βˆ’ ADP bibechana-46416 143 1 ln{erf[Ο‰1 ln{erf[Ο‰1 ADV bibechana-46416 143 2 + + CCONJ bibechana-46416 143 3 Ξ³2 Ξ³2 ADJ bibechana-46416 143 4 + + CCONJ bibechana-46416 143 5 Ο‰2 Ο‰2 ADJ bibechana-46416 143 6 ] ] X bibechana-46416 143 7 } } PUNCT bibechana-46416 143 8 + + CCONJ bibechana-46416 143 9 ln{ΞΎ ln{ΞΎ NOUN bibechana-46416 143 10 } } PUNCT bibechana-46416 143 11 ] ] PUNCT bibechana-46416 143 12 ) ) PUNCT bibechana-46416 143 13 ( ( PUNCT bibechana-46416 143 14 16 16 NUM bibechana-46416 143 15 ) ) PUNCT bibechana-46416 143 16 ( ( PUNCT bibechana-46416 143 17 16 16 NUM bibechana-46416 143 18 ) ) PUNCT bibechana-46416 143 19 2.3.4 2.3.4 NUM bibechana-46416 143 20 . . PUNCT bibechana-46416 143 21 vibrational vibrational ADJ bibechana-46416 143 22 entropy entropy NOUN bibechana-46416 143 23 of of ADP bibechana-46416 143 24 q q NOUN bibechana-46416 143 25 - - PUNCT bibechana-46416 143 26 deformed deform VERB bibechana-46416 143 27 hp hp NOUN bibechana-46416 143 28 ( ( PUNCT bibechana-46416 143 29 veqhp veqhp NOUN bibechana-46416 143 30 ) ) PUNCT bibechana-46416 143 31 the the DET bibechana-46416 143 32 vibrational vibrational ADJ bibechana-46416 143 33 entropy entropy NOUN bibechana-46416 143 34 is be AUX bibechana-46416 143 35 obtained obtain VERB bibechana-46416 143 36 as as ADP bibechana-46416 143 37 𝑆(𝛽 𝑆(𝛽 PROPN bibechana-46416 143 38 ) ) PUNCT bibechana-46416 143 39 = = PUNCT bibechana-46416 143 40 π‘˜π‘™π‘›(𝑍𝑣𝑖𝑏(𝛽 π‘˜π‘™π‘›(𝑍𝑣𝑖𝑏(𝛽 NOUN bibechana-46416 143 41 ) ) PUNCT bibechana-46416 143 42 ) ) PUNCT bibechana-46416 144 1 + + CCONJ bibechana-46416 145 1 π‘˜π‘‡ π‘˜π‘‡ PROPN bibechana-46416 145 2 πœ• πœ• PROPN bibechana-46416 145 3 πœ•π›½ πœ•π›½ PROPN bibechana-46416 145 4 ( ( PUNCT bibechana-46416 145 5 𝑙𝑛𝑍𝑣𝑖𝑏(𝛽 𝑙𝑛𝑍𝑣𝑖𝑏(𝛽 NOUN bibechana-46416 145 6 ) ) PUNCT bibechana-46416 145 7 ) ) PUNCT bibechana-46416 145 8 𝑆(𝛽 𝑆(𝛽 PROPN bibechana-46416 145 9 ) ) PUNCT bibechana-46416 145 10 = = SYM bibechana-46416 145 11 π‘˜π‘™π‘› π‘˜π‘™π‘› PROPN bibechana-46416 145 12 ( ( PUNCT bibechana-46416 145 13 π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ NOUN bibechana-46416 145 14 ( ( PUNCT bibechana-46416 145 15 βˆ’ βˆ’ X bibechana-46416 145 16 erf[Ξ³1 erf[Ξ³1 PROPN bibechana-46416 145 17 βˆ’ βˆ’ PROPN bibechana-46416 145 18 Ξ³2 Ξ³2 NOUN bibechana-46416 145 19 ] ] X bibechana-46416 145 20 + + CCONJ bibechana-46416 145 21 𝑒 𝑒 PROPN bibechana-46416 145 22 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 NUM bibechana-46416 145 23 + + CCONJ bibechana-46416 145 24 Ξ³2 Ξ³2 ADJ bibechana-46416 145 25 ] ] PUNCT bibechana-46416 145 26 βˆ’ βˆ’ PROPN bibechana-46416 145 27 erf[Ο‰1 erf[Ο‰1 PROPN bibechana-46416 145 28 + + CCONJ bibechana-46416 145 29 Ξ³2 Ξ³2 PROPN bibechana-46416 145 30 + + ADJ bibechana-46416 145 31 Ο‰2 Ο‰2 ADJ bibechana-46416 145 32 ] ] PUNCT bibechana-46416 145 33 ) ) PUNCT bibechana-46416 145 34 βˆ’ βˆ’ ADP bibechana-46416 145 35 ΞΎ ΞΎ X bibechana-46416 145 36 ) ) PUNCT bibechana-46416 145 37 4βˆšβˆ’π‘Žπ›½ 4βˆšβˆ’π‘Žπ›½ NOUN bibechana-46416 145 38 ) ) PUNCT bibechana-46416 146 1 + + CCONJ bibechana-46416 146 2 π‘˜π‘‡ π‘˜π‘‡ PROPN bibechana-46416 146 3 πœ• πœ• NOUN bibechana-46416 146 4 πœ•π›½ πœ•π›½ PROPN bibechana-46416 146 5 ( ( PUNCT bibechana-46416 146 6 π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ π‘’π‘π›½βˆ’2βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½βˆšπœ‹ X bibechana-46416 146 7 ( ( PUNCT bibechana-46416 146 8 βˆ’ βˆ’ PROPN bibechana-46416 146 9 erf[Ξ³1 erf[Ξ³1 PROPN bibechana-46416 146 10 βˆ’ βˆ’ PROPN bibechana-46416 146 11 Ξ³2 Ξ³2 NOUN bibechana-46416 146 12 ] ] X bibechana-46416 147 1 + + CCONJ bibechana-46416 147 2 𝑒 𝑒 PROPN bibechana-46416 147 3 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 4βˆšβˆ’π‘Žπ›½βˆšβˆ’π‘π›½(erf[Ξ³1 NUM bibechana-46416 147 4 + + CCONJ bibechana-46416 147 5 Ξ³2 Ξ³2 ADJ bibechana-46416 147 6 ] ] PUNCT bibechana-46416 147 7 βˆ’ βˆ’ PROPN bibechana-46416 148 1 erf[Ο‰1 erf[Ο‰1 PROPN bibechana-46416 148 2 + + CCONJ bibechana-46416 148 3 Ξ³2 Ξ³2 ADJ bibechana-46416 148 4 + + CCONJ bibechana-46416 148 5 Ο‰2 Ο‰2 NUM bibechana-46416 148 6 ] ] PUNCT bibechana-46416 148 7 ) ) PUNCT bibechana-46416 148 8 βˆ’ βˆ’ ADP bibechana-46416 148 9 ΞΎ ΞΎ X bibechana-46416 148 10 ) ) PUNCT bibechana-46416 148 11 4βˆšβˆ’π‘Žπ›½ 4βˆšβˆ’π‘Žπ›½ NOUN bibechana-46416 148 12 ) ) PUNCT bibechana-46416 148 13 𝑆(𝛽 𝑆(𝛽 PROPN bibechana-46416 148 14 ) ) PUNCT bibechana-46416 148 15 = = VERB bibechana-46416 149 1 π‘˜[ln π‘˜[ln NOUN bibechana-46416 149 2 { { PUNCT bibechana-46416 149 3 ( ( PUNCT bibechana-46416 149 4 π‘’π‘Ÿπ‘“[𝛀2 π‘’π‘Ÿπ‘“[𝛀2 PROPN bibechana-46416 149 5 βˆ’ βˆ’ PROPN bibechana-46416 149 6 𝛀2 𝛀2 PROPN bibechana-46416 149 7 ] ] X bibechana-46416 149 8 ) ) PUNCT bibechana-46416 149 9 } } PUNCT bibechana-46416 150 1 + + CCONJ bibechana-46416 150 2 ln{erf[Ξ³1 ln{erf[Ξ³1 X bibechana-46416 150 3 + + X bibechana-46416 150 4 Ξ³2 Ξ³2 ADJ bibechana-46416 150 5 ] ] X bibechana-46416 150 6 } } PUNCT bibechana-46416 150 7 βˆ’ βˆ’ ADP bibechana-46416 151 1 ln{erf[Ο‰1 ln{erf[Ο‰1 ADV bibechana-46416 151 2 + + CCONJ bibechana-46416 151 3 Ξ³2 Ξ³2 ADJ bibechana-46416 151 4 + + CCONJ bibechana-46416 151 5 Ο‰2 Ο‰2 ADJ bibechana-46416 151 6 ] ] X bibechana-46416 151 7 } } PUNCT bibechana-46416 151 8 + + CCONJ bibechana-46416 151 9 ln{ΞΎ ln{ΞΎ NOUN bibechana-46416 151 10 } } PUNCT bibechana-46416 151 11 ] ] PUNCT bibechana-46416 152 1 + + CCONJ bibechana-46416 152 2 π‘˜π‘‡ π‘˜π‘‡ PROPN bibechana-46416 152 3 𝑑(ln 𝑑(ln NUM bibechana-46416 152 4 { { PUNCT bibechana-46416 152 5 ( ( PUNCT bibechana-46416 152 6 π‘’π‘Ÿπ‘“[𝛀2βˆ’π›€2 π‘’π‘Ÿπ‘“[𝛀2βˆ’π›€2 PROPN bibechana-46416 152 7 ] ] NOUN bibechana-46416 152 8 ) ) PUNCT bibechana-46416 152 9 } } PUNCT bibechana-46416 152 10 ) ) PUNCT bibechana-46416 152 11 𝑑𝛽 𝑑𝛽 VERB bibechana-46416 153 1 + + CCONJ bibechana-46416 153 2 𝑑 𝑑 PROPN bibechana-46416 153 3 ln{erf[Ξ³1+Ξ³2 ln{erf[Ξ³1+Ξ³2 PROPN bibechana-46416 153 4 ] ] PUNCT bibechana-46416 153 5 } } PUNCT bibechana-46416 153 6 𝑑𝛽 𝑑𝛽 ADP bibechana-46416 153 7 βˆ’ βˆ’ PROPN bibechana-46416 153 8 𝑑 𝑑 PROPN bibechana-46416 153 9 ln{erf[Ο‰1+Ξ³2+Ο‰2 ln{erf[Ο‰1+Ξ³2+Ο‰2 PROPN bibechana-46416 153 10 ] ] X bibechana-46416 153 11 } } PUNCT bibechana-46416 153 12 𝑑𝛽 𝑑𝛽 INTJ bibechana-46416 153 13 ( ( PUNCT bibechana-46416 153 14 17 17 NUM bibechana-46416 153 15 ) ) PUNCT bibechana-46416 153 16 thermodynamical thermodynamical ADJ bibechana-46416 153 17 properties property NOUN bibechana-46416 153 18 have have VERB bibechana-46416 153 19 error error NOUN bibechana-46416 153 20 functions function NOUN bibechana-46416 153 21 with with ADP bibechana-46416 153 22 different different ADJ bibechana-46416 153 23 parameters parameter NOUN bibechana-46416 153 24 and and CCONJ bibechana-46416 153 25 in in ADP bibechana-46416 153 26 literature literature NOUN bibechana-46416 154 1 [ [ X bibechana-46416 154 2 9 9 NUM bibechana-46416 154 3 ] ] PUNCT bibechana-46416 154 4 authors author NOUN bibechana-46416 154 5 discuss discuss VERB bibechana-46416 154 6 its its PRON bibechana-46416 154 7 multiuse multiuse NOUN bibechana-46416 154 8 use use NOUN bibechana-46416 154 9 . . PUNCT bibechana-46416 155 1 therefore therefore ADV bibechana-46416 155 2 , , PUNCT bibechana-46416 155 3 studying study VERB bibechana-46416 155 4 the the DET bibechana-46416 155 5 thermodynamic thermodynamic ADJ bibechana-46416 155 6 properties property NOUN bibechana-46416 155 7 for for ADP bibechana-46416 155 8 consideration consideration NOUN bibechana-46416 155 9 in in ADP bibechana-46416 155 10 this this DET bibechana-46416 155 11 paper paper NOUN bibechana-46416 155 12 has have VERB bibechana-46416 155 13 equal equal ADJ bibechana-46416 155 14 importance importance NOUN bibechana-46416 155 15 as as SCONJ bibechana-46416 155 16 discussed discuss VERB bibechana-46416 155 17 in in ADP bibechana-46416 155 18 the the DET bibechana-46416 155 19 literature literature NOUN bibechana-46416 155 20 [ [ X bibechana-46416 155 21 8 8 NUM bibechana-46416 155 22 , , PUNCT bibechana-46416 155 23 9 9 NUM bibechana-46416 155 24 ] ] PUNCT bibechana-46416 155 25 . . PUNCT bibechana-46416 156 1 the the DET bibechana-46416 156 2 thermodynamic thermodynamic ADJ bibechana-46416 156 3 properties property NOUN bibechana-46416 156 4 of of ADP bibechana-46416 156 5 the the DET bibechana-46416 156 6 electron electron NOUN bibechana-46416 156 7 in in ADP bibechana-46416 156 8 considering consider VERB bibechana-46416 156 9 potential potential NOUN bibechana-46416 156 10 is be AUX bibechana-46416 156 11 obtained obtain VERB bibechana-46416 156 12 in in ADP bibechana-46416 156 13 equation equation NOUN bibechana-46416 156 14 ( ( PUNCT bibechana-46416 156 15 14 14 NUM bibechana-46416 156 16 ) ) PUNCT bibechana-46416 156 17 , , PUNCT bibechana-46416 156 18 ( ( PUNCT bibechana-46416 156 19 15 15 NUM bibechana-46416 156 20 ) ) PUNCT bibechana-46416 156 21 , , PUNCT bibechana-46416 156 22 ( ( PUNCT bibechana-46416 156 23 16 16 NUM bibechana-46416 156 24 ) ) PUNCT bibechana-46416 156 25 , , PUNCT bibechana-46416 156 26 and and CCONJ bibechana-46416 156 27 ( ( PUNCT bibechana-46416 156 28 17 17 NUM bibechana-46416 156 29 ) ) PUNCT bibechana-46416 156 30 showing show VERB bibechana-46416 156 31 that that SCONJ bibechana-46416 156 32 the the DET bibechana-46416 156 33 thermodynamic thermodynamic ADJ bibechana-46416 156 34 properties property NOUN bibechana-46416 156 35 depend depend VERB bibechana-46416 156 36 upon upon SCONJ bibechana-46416 156 37 quantum quantum ADJ bibechana-46416 156 38 number number NOUN bibechana-46416 156 39 also also ADV bibechana-46416 156 40 . . PUNCT bibechana-46416 157 1 therefore therefore ADV bibechana-46416 157 2 , , PUNCT bibechana-46416 157 3 the the DET bibechana-46416 157 4 thermodynamic thermodynamic ADJ bibechana-46416 157 5 properties property NOUN bibechana-46416 157 6 for for ADP bibechana-46416 157 7 considering consider VERB bibechana-46416 157 8 potential potential ADJ bibechana-46416 157 9 depend depend VERB bibechana-46416 157 10 upon upon SCONJ bibechana-46416 157 11 quantum quantum ADJ bibechana-46416 157 12 number number NOUN bibechana-46416 157 13 as as ADV bibechana-46416 157 14 well well ADV bibechana-46416 157 15 as as ADP bibechana-46416 157 16 temperature temperature NOUN bibechana-46416 157 17 . . PUNCT bibechana-46416 158 1 3 3 X bibechana-46416 158 2 . . X bibechana-46416 158 3 conclusion conclusion VERB bibechana-46416 158 4 the the DET bibechana-46416 158 5 development development NOUN bibechana-46416 158 6 of of ADP bibechana-46416 158 7 energy energy NOUN bibechana-46416 158 8 eigenvalue eigenvalue NOUN bibechana-46416 158 9 for for ADP bibechana-46416 158 10 q q ADJ bibechana-46416 158 11 - - PUNCT bibechana-46416 158 12 deformation deformation NOUN bibechana-46416 158 13 hp hp ADJ bibechana-46416 158 14 potential potential NOUN bibechana-46416 158 15 develops develop VERB bibechana-46416 158 16 in in ADP bibechana-46416 158 17 equation equation NOUN bibechana-46416 158 18 ( ( PUNCT bibechana-46416 158 19 8) 8) NUM bibechana-46416 158 20 with with ADP bibechana-46416 158 21 the the DET bibechana-46416 158 22 help help NOUN bibechana-46416 158 23 of of ADP bibechana-46416 158 24 this this DET bibechana-46416 158 25 energy energy NOUN bibechana-46416 158 26 vibrational vibrational ADJ bibechana-46416 158 27 thermodynamic thermodynamic ADJ bibechana-46416 158 28 properties property NOUN bibechana-46416 158 29 are be AUX bibechana-46416 158 30 calculated calculate VERB bibechana-46416 158 31 . . PUNCT bibechana-46416 159 1 the the DET bibechana-46416 159 2 development development NOUN bibechana-46416 159 3 of of ADP bibechana-46416 159 4 a a DET bibechana-46416 159 5 mathematical mathematical ADJ bibechana-46416 159 6 model model NOUN bibechana-46416 159 7 for for ADP bibechana-46416 159 8 thermodynamic thermodynamic ADJ bibechana-46416 159 9 properties property NOUN bibechana-46416 159 10 for for ADP bibechana-46416 159 11 the the DET bibechana-46416 159 12 electron electron NOUN bibechana-46416 159 13 in in ADP bibechana-46416 159 14 q q ADJ bibechana-46416 159 15 - - PUNCT bibechana-46416 159 16 deformation deformation NOUN bibechana-46416 159 17 potential potential NOUN bibechana-46416 159 18 is be AUX bibechana-46416 159 19 completely completely ADV bibechana-46416 159 20 new new ADJ bibechana-46416 159 21 . . PUNCT bibechana-46416 160 1 in in ADP bibechana-46416 160 2 addition addition NOUN bibechana-46416 160 3 , , PUNCT bibechana-46416 160 4 the the DET bibechana-46416 160 5 thermodynamic thermodynamic ADJ bibechana-46416 160 6 properties property NOUN bibechana-46416 160 7 also also ADV bibechana-46416 160 8 depend depend VERB bibechana-46416 160 9 upon upon SCONJ bibechana-46416 160 10 the the DET bibechana-46416 160 11 quantum quantum ADJ bibechana-46416 160 12 number number NOUN bibechana-46416 160 13 which which PRON bibechana-46416 160 14 means mean VERB bibechana-46416 160 15 vary vary VERB bibechana-46416 160 16 with with ADP bibechana-46416 160 17 the the DET bibechana-46416 160 18 quantum quantum ADJ bibechana-46416 160 19 number number NOUN bibechana-46416 160 20 . . PUNCT bibechana-46416 161 1 for for ADP bibechana-46416 161 2 example example NOUN bibechana-46416 161 3 , , PUNCT bibechana-46416 161 4 the the DET bibechana-46416 161 5 thermodynamic thermodynamic ADJ bibechana-46416 161 6 properties property NOUN bibechana-46416 161 7 of of ADP bibechana-46416 161 8 the the DET bibechana-46416 161 9 electron electron NOUN bibechana-46416 161 10 in in ADP bibechana-46416 161 11 the the DET bibechana-46416 161 12 n=1 n=1 PROPN bibechana-46416 161 13 orbit orbit NOUN bibechana-46416 161 14 are be AUX bibechana-46416 161 15 different different ADJ bibechana-46416 161 16 from from ADP bibechana-46416 161 17 the the DET bibechana-46416 161 18 thermodynamic thermodynamic ADJ bibechana-46416 161 19 properties property NOUN bibechana-46416 161 20 of of ADP bibechana-46416 161 21 the the DET bibechana-46416 161 22 electron electron NOUN bibechana-46416 161 23 in in ADP bibechana-46416 161 24 the the DET bibechana-46416 161 25 n=2 n=2 ADJ bibechana-46416 161 26 orbit orbit NOUN bibechana-46416 161 27 and and CCONJ bibechana-46416 161 28 so so ADV bibechana-46416 161 29 on on ADV bibechana-46416 161 30 . . PUNCT bibechana-46416 162 1 this this PRON bibechana-46416 162 2 is be AUX bibechana-46416 162 3 because because SCONJ bibechana-46416 162 4 the the DET bibechana-46416 162 5 thermodynamic thermodynamic ADJ bibechana-46416 162 6 properties property NOUN bibechana-46416 162 7 depend depend VERB bibechana-46416 162 8 upon upon SCONJ bibechana-46416 162 9 the the DET bibechana-46416 162 10 energy energy NOUN bibechana-46416 162 11 eigenvalue eigenvalue NOUN bibechana-46416 162 12 of of ADP bibechana-46416 162 13 the the DET bibechana-46416 162 14 electron electron NOUN bibechana-46416 162 15 and and CCONJ bibechana-46416 162 16 the the DET bibechana-46416 162 17 energy energy NOUN bibechana-46416 162 18 eigenvalue eigenvalue NOUN bibechana-46416 162 19 of of ADP bibechana-46416 162 20 the the DET bibechana-46416 162 21 electron electron NOUN bibechana-46416 162 22 depends depend VERB bibechana-46416 162 23 upon upon SCONJ bibechana-46416 162 24 the the DET bibechana-46416 162 25 quantum quantum ADJ bibechana-46416 162 26 number number NOUN bibechana-46416 162 27 . . PUNCT bibechana-46416 163 1 the the DET bibechana-46416 163 2 developed develop VERB bibechana-46416 163 3 mathematical mathematical ADJ bibechana-46416 163 4 model model NOUN bibechana-46416 163 5 is be AUX bibechana-46416 163 6 based base VERB bibechana-46416 163 7 on on ADP bibechana-46416 163 8 a a DET bibechana-46416 163 9 gaussian gaussian ADJ bibechana-46416 163 10 hypergeometric hypergeometric ADJ bibechana-46416 163 11 function function NOUN bibechana-46416 163 12 with with ADP bibechana-46416 163 13 a a DET bibechana-46416 163 14 partition partition NOUN bibechana-46416 163 15 function function NOUN bibechana-46416 163 16 . . PUNCT bibechana-46416 164 1 to to PART bibechana-46416 164 2 study study VERB bibechana-46416 164 3 the the DET bibechana-46416 164 4 more more ADV bibechana-46416 164 5 detailed detailed ADJ bibechana-46416 164 6 thermodynamic thermodynamic ADJ bibechana-46416 164 7 properties property NOUN bibechana-46416 164 8 of of ADP bibechana-46416 164 9 an an DET bibechana-46416 164 10 electron electron NOUN bibechana-46416 164 11 in in ADP bibechana-46416 164 12 considering consider VERB bibechana-46416 164 13 potential potential ADJ bibechana-46416 164 14 one one PRON bibechana-46416 164 15 may may AUX bibechana-46416 164 16 extend extend VERB bibechana-46416 164 17 the the DET bibechana-46416 164 18 development development NOUN bibechana-46416 164 19 theory theory NOUN bibechana-46416 164 20 because because SCONJ bibechana-46416 164 21 due due ADP bibechana-46416 164 22 to to ADP bibechana-46416 164 23 the the DET bibechana-46416 164 24 complexity complexity NOUN bibechana-46416 164 25 of of ADP bibechana-46416 164 26 mathematical mathematical ADJ bibechana-46416 164 27 derivation derivation NOUN bibechana-46416 164 28 authors author NOUN bibechana-46416 164 29 consider consider VERB bibechana-46416 164 30 the the DET bibechana-46416 164 31 limitations limitation NOUN bibechana-46416 164 32 of of ADP bibechana-46416 164 33 their their PRON bibechana-46416 164 34 work work NOUN bibechana-46416 164 35 . . PUNCT bibechana-46416 165 1 acknowledgment acknowledgment NOUN bibechana-46416 165 2 the the DET bibechana-46416 165 3 authors author NOUN bibechana-46416 165 4 would would AUX bibechana-46416 165 5 like like VERB bibechana-46416 165 6 to to PART bibechana-46416 165 7 thank thank VERB bibechana-46416 165 8 the the DET bibechana-46416 165 9 department department PROPN bibechana-46416 165 10 of of ADP bibechana-46416 165 11 physics physics PROPN bibechana-46416 165 12 , , PUNCT bibechana-46416 165 13 tri tri PROPN bibechana-46416 165 14 - - ADJ bibechana-46416 165 15 chandra chandra PROPN bibechana-46416 165 16 multiple multiple ADJ bibechana-46416 165 17 campus campus PROPN bibechana-46416 165 18 , , PUNCT bibechana-46416 165 19 tribhuvan tribhuvan PROPN bibechana-46416 165 20 university university PROPN bibechana-46416 165 21 and and CCONJ bibechana-46416 165 22 patan patan ADJ bibechana-46416 165 23 multiple multiple ADJ bibechana-46416 165 24 campus campus PROPN bibechana-46416 165 25 , , PUNCT bibechana-46416 165 26 tribhuvan tribhuvan PROPN bibechana-46416 165 27 university university PROPN bibechana-46416 165 28 , , PUNCT bibechana-46416 165 29 nepal nepal ADJ bibechana-46416 165 30 ; ; PUNCT bibechana-46416 165 31 innovative innovative ADJ bibechana-46416 165 32 ghar ghar NOUN bibechana-46416 165 33 nepal nepal NOUN bibechana-46416 165 34 , , PUNCT bibechana-46416 165 35 and and CCONJ bibechana-46416 165 36 national national PROPN bibechana-46416 165 37 research research PROPN bibechana-46416 165 38 council council PROPN bibechana-46416 165 39 nepal nepal NOUN bibechana-46416 165 40 for for ADP bibechana-46416 165 41 supporting support VERB bibechana-46416 165 42 this this DET bibechana-46416 165 43 work work NOUN bibechana-46416 165 44 . . PUNCT bibechana-46416 166 1 references reference NOUN bibechana-46416 166 2 [ [ X bibechana-46416 166 3 1 1 NUM bibechana-46416 166 4 ] ] X bibechana-46416 166 5 c.o c.o PROPN bibechana-46416 166 6 . . PROPN bibechana-46416 166 7 edet edet PROPN bibechana-46416 166 8 and and CCONJ bibechana-46416 166 9 p.o p.o PROPN bibechana-46416 166 10 . . PROPN bibechana-46416 166 11 okoi okoi PROPN bibechana-46416 166 12 , , PUNCT bibechana-46416 166 13 any any DET bibechana-46416 166 14 l l ADJ bibechana-46416 166 15 - - ADJ bibechana-46416 166 16 state state NOUN bibechana-46416 166 17 solutions solution NOUN bibechana-46416 166 18 of of ADP bibechana-46416 166 19 the the DET bibechana-46416 166 20 schrodinger schrodinger ADJ bibechana-46416 166 21 equation equation NOUN bibechana-46416 166 22 for for ADP bibechana-46416 166 23 q q ADV bibechana-46416 166 24 - - PUNCT bibechana-46416 166 25 deformed deform VERB bibechana-46416 166 26 hulthen hulthen ADV bibechana-46416 166 27 plus plus CCONJ bibechana-46416 166 28 generalized generalized ADJ bibechana-46416 166 29 inverse inverse ADJ bibechana-46416 166 30 quadratic quadratic ADJ bibechana-46416 166 31 yukawa yukawa PROPN bibechana-46416 166 32 potential potential NOUN bibechana-46416 166 33 in in ADP bibechana-46416 166 34 arbitrary arbitrary ADJ bibechana-46416 166 35 dimensions dimension NOUN bibechana-46416 166 36 , , PUNCT bibechana-46416 166 37 revista revista VERB bibechana-46416 166 38 mexicana mexicana PROPN bibechana-46416 166 39 de de PROPN bibechana-46416 166 40 fΔ±sica fΔ±sica PROPN bibechana-46416 166 41 , , PUNCT bibechana-46416 166 42 65(2019)333 65(2019)333 PROPN bibechana-46416 166 43 - - PUNCT bibechana-46416 166 44 344 344 NUM bibechana-46416 166 45 , , PUNCT bibechana-46416 166 46 http://www.scielo.org.mx/pdf/rmf/v65n4/0035-001x-rmf-6504-333.pdf http://www.scielo.org.mx/pdf/rmf/v65n4/0035-001x-rmf-6504-333.pdf NOUN bibechana-46416 166 47 [ [ X bibechana-46416 166 48 2 2 NUM bibechana-46416 166 49 ] ] PUNCT bibechana-46416 166 50 i. i. PROPN bibechana-46416 166 51 b. b. PROPN bibechana-46416 166 52 okon okon PROPN bibechana-46416 166 53 , , PUNCT bibechana-46416 166 54 o. o. PROPN bibechana-46416 166 55 popoola popoola PROPN bibechana-46416 166 56 , , PUNCT bibechana-46416 166 57 and and CCONJ bibechana-46416 166 58 c. c. PROPN bibechana-46416 166 59 n. n. PROPN bibechana-46416 166 60 isonguyo isonguyo PROPN bibechana-46416 166 61 , , PUNCT bibechana-46416 166 62 approximate approximate ADJ bibechana-46416 166 63 solutions solution NOUN bibechana-46416 166 64 of of ADP bibechana-46416 166 65 schrodinger schrodinger ADJ bibechana-46416 166 66 equation equation NOUN bibechana-46416 166 67 with with ADP bibechana-46416 166 68 some some DET bibechana-46416 166 69 diatomic diatomic ADJ bibechana-46416 166 70 molecular molecular ADJ bibechana-46416 166 71 interactions interaction NOUN bibechana-46416 166 72 using use VERB bibechana-46416 166 73 nikiforov nikiforov NOUN bibechana-46416 166 74 - - PUNCT bibechana-46416 166 75 uvarov uvarov ADJ bibechana-46416 166 76 method method NOUN bibechana-46416 166 77 , , PUNCT bibechana-46416 166 78 advance advance NOUN bibechana-46416 166 79 in in ADP bibechana-46416 166 80 high high ADJ bibechana-46416 166 81 energy energy NOUN bibechana-46416 166 82 physics physics NOUN bibechana-46416 166 83 , , PUNCT bibechana-46416 166 84 volume volume NOUN bibechana-46416 166 85 2017 2017 NUM bibechana-46416 166 86 , , PUNCT bibechana-46416 166 87 article article NOUN bibechana-46416 166 88 i i PROPN bibechana-46416 166 89 d d PROPN bibechana-46416 166 90 9671816(2017)1 9671816(2017)1 PROPN bibechana-46416 166 91 - - PUNCT bibechana-46416 166 92 24 24 NUM bibechana-46416 166 93 . . PUNCT bibechana-46416 167 1 https://doi.org/10.1155/2017/9671816 https://doi.org/10.1155/2017/9671816 PRON bibechana-46416 168 1 [ [ X bibechana-46416 168 2 3 3 X bibechana-46416 168 3 ] ] X bibechana-46416 168 4 l. l. PROPN bibechana-46416 168 5 hulthen hulthen PROPN bibechana-46416 168 6 , , PUNCT bibechana-46416 168 7 uber uber ADJ bibechana-46416 168 8 die die NOUN bibechana-46416 168 9 eigenlosungen eigenlosungen PROPN bibechana-46416 168 10 der der PROPN bibechana-46416 168 11 schrodingergleichung schrodingergleichung PROPN bibechana-46416 168 12 des des PROPN bibechana-46416 168 13 deuterons deuterons PROPN bibechana-46416 168 14 , , PUNCT bibechana-46416 168 15 arkiv arkiv ADP bibechana-46416 168 16 fΓΆr fΓΆr PROPN bibechana-46416 168 17 matematik matematik PROPN bibechana-46416 168 18 , , PUNCT bibechana-46416 168 19 astronomi astronomi PROPN bibechana-46416 168 20 och och PROPN bibechana-46416 168 21 fysik fysik PROPN bibechana-46416 168 22 , , PUNCT bibechana-46416 168 23 28a 28a NUM bibechana-46416 168 24 , , PUNCT bibechana-46416 168 25 14 14 NUM bibechana-46416 168 26 ( ( PUNCT bibechana-46416 168 27 1942)1 1942)1 NUM bibechana-46416 168 28 - - SYM bibechana-46416 168 29 12 12 NUM bibechana-46416 168 30 . . PUNCT bibechana-46416 169 1 [ [ X bibechana-46416 169 2 4 4 X bibechana-46416 169 3 ] ] X bibechana-46416 169 4 s. s. PROPN bibechana-46416 169 5 flugge flugge PROPN bibechana-46416 169 6 , , PUNCT bibechana-46416 169 7 practical practical ADJ bibechana-46416 169 8 quantum quantum ADJ bibechana-46416 169 9 mechanics mechanic NOUN bibechana-46416 169 10 , , PUNCT bibechana-46416 169 11 springer springer NOUN bibechana-46416 169 12 - - PUNCT bibechana-46416 169 13 verlag verlag PROPN bibechana-46416 169 14 , , PUNCT bibechana-46416 169 15 berlin berlin PROPN bibechana-46416 169 16 heidelberg heidelberg PROPN bibechana-46416 169 17 ( ( PUNCT bibechana-46416 169 18 1999 1999 NUM bibechana-46416 169 19 ) ) PUNCT bibechana-46416 169 20 . . PUNCT bibechana-46416 170 1 [ [ X bibechana-46416 170 2 5 5 X bibechana-46416 170 3 ] ] PUNCT bibechana-46416 170 4 r. r. PROPN bibechana-46416 170 5 l. l. PROPN bibechana-46416 170 6 hall hall PROPN bibechana-46416 170 7 , , PUNCT bibechana-46416 170 8 n. n. PROPN bibechana-46416 170 9 saad saad PROPN bibechana-46416 170 10 and and CCONJ bibechana-46416 170 11 k. k. PROPN bibechana-46416 170 12 d. d. PROPN bibechana-46416 170 13 sen sen PROPN bibechana-46416 170 14 , , PUNCT bibechana-46416 170 15 exact exact ADJ bibechana-46416 170 16 normalized normalize VERB bibechana-46416 170 17 eigenfunctions eigenfunction NOUN bibechana-46416 170 18 for for ADP bibechana-46416 170 19 general general ADJ bibechana-46416 170 20 deformed deform VERB bibechana-46416 170 21 hulthen hulthen NOUN bibechana-46416 170 22 potentials potential NOUN bibechana-46416 170 23 , , PUNCT bibechana-46416 170 24 2018 2018 NUM bibechana-46416 170 25 , , PUNCT bibechana-46416 170 26 1 1 NUM bibechana-46416 170 27 - - SYM bibechana-46416 170 28 4 4 NUM bibechana-46416 170 29 https://arxiv.org/pdf/1812.06383.pdf https://arxiv.org/pdf/1812.06383.pdf NOUN bibechana-46416 170 30 [ [ X bibechana-46416 170 31 6 6 NUM bibechana-46416 170 32 ] ] X bibechana-46416 170 33 u. u. PROPN bibechana-46416 170 34 s. s. PROPN bibechana-46416 170 35 okorie okorie PROPN bibechana-46416 170 36 , , PUNCT bibechana-46416 170 37 a. a. PROPN bibechana-46416 170 38 n. n. PROPN bibechana-46416 170 39 ikot ikot PROPN bibechana-46416 170 40 , , PUNCT bibechana-46416 170 41 e. e. PROPN bibechana-46416 170 42 o. o. PROPN bibechana-46416 170 43 chukwuocha chukwuocha PROPN bibechana-46416 170 44 , , PUNCT bibechana-46416 170 45 thermodynamic thermodynamic ADJ bibechana-46416 170 46 properties property NOUN bibechana-46416 170 47 of of ADP bibechana-46416 170 48 improved improved ADJ bibechana-46416 170 49 deformed deform VERB bibechana-46416 170 50 exponentialtype exponentialtype NOUN bibechana-46416 170 51 potential potential NOUN bibechana-46416 170 52 ( ( PUNCT bibechana-46416 170 53 idea idea NOUN bibechana-46416 170 54 ) ) PUNCT bibechana-46416 170 55 for for ADP bibechana-46416 170 56 some some DET bibechana-46416 170 57 diatomic diatomic ADJ bibechana-46416 170 58 molecules molecule NOUN bibechana-46416 170 59 , , PUNCT bibechana-46416 170 60 accessed access VERB bibechana-46416 170 61 at at ADP bibechana-46416 170 62 1st 1st ADJ bibechana-46416 170 63 june june PROPN bibechana-46416 170 64 2021 2021 NUM bibechana-46416 170 65 https://arxiv.org/ftp/arxiv/papers/2001/2001.04799.pdf https://arxiv.org/ftp/arxiv/papers/2001/2001.04799.pdf PROPN bibechana-46416 171 1 [ [ X bibechana-46416 171 2 7 7 NUM bibechana-46416 171 3 ] ] PUNCT bibechana-46416 171 4 m. m. NOUN bibechana-46416 171 5 a. a. PROPN bibechana-46416 171 6 shady shady PROPN bibechana-46416 171 7 , , PUNCT bibechana-46416 171 8 t. t. PROPN bibechana-46416 171 9 a. a. PROPN bibechana-46416 171 10 a. a. PROPN bibechana-46416 171 11 karim karim PROPN bibechana-46416 171 12 and and CCONJ bibechana-46416 171 13 sy sy PROPN bibechana-46416 171 14 e. e. PROPN bibechana-46416 171 15 alarab alarab PROPN bibechana-46416 171 16 , , PUNCT bibechana-46416 171 17 masses masse NOUN bibechana-46416 171 18 and and CCONJ bibechana-46416 171 19 thermodynamic thermodynamic ADJ bibechana-46416 171 20 properties property NOUN bibechana-46416 171 21 of of ADP bibechana-46416 171 22 heavy heavy ADJ bibechana-46416 171 23 mesons meson NOUN bibechana-46416 171 24 in in ADP bibechana-46416 171 25 the the DET bibechana-46416 171 26 nonrelativistic nonrelativistic ADJ bibechana-46416 171 27 quark quark NOUN bibechana-46416 171 28 model model NOUN bibechana-46416 171 29 using use VERB bibechana-46416 171 30 the the DET bibechana-46416 171 31 nikiforov nikiforov NOUN bibechana-46416 171 32 – – PUNCT bibechana-46416 171 33 uvarov uvarov ADJ bibechana-46416 171 34 method method NOUN bibechana-46416 171 35 , , PUNCT bibechana-46416 171 36 journal journal NOUN bibechana-46416 171 37 of of ADP bibechana-46416 171 38 the the DET bibechana-46416 171 39 egyptian egyptian PROPN bibechana-46416 171 40 mathematical mathematical PROPN bibechana-46416 171 41 society society NOUN bibechana-46416 171 42 , , PUNCT bibechana-46416 171 43 27(14)(2019 27(14)(2019 NUM bibechana-46416 171 44 ) ) PUNCT bibechana-46416 171 45 1 1 NUM bibechana-46416 171 46 - - SYM bibechana-46416 171 47 15 15 NUM bibechana-46416 171 48 , , PUNCT bibechana-46416 171 49 https://doi.org/10.1186/s42787-019-0014-0 https://doi.org/10.1186/s42787-019-0014-0 NUM bibechana-46416 171 50 [ [ SYM bibechana-46416 171 51 8 8 NUM bibechana-46416 171 52 ] ] X bibechana-46416 171 53 u. u. PROPN bibechana-46416 171 54 s. s. PROPN bibechana-46416 171 55 okorie okorie PROPN bibechana-46416 171 56 , , PUNCT bibechana-46416 171 57 e. e. PROPN bibechana-46416 171 58 e. e. PROPN bibechana-46416 171 59 ibekwe ibekwe PROPN bibechana-46416 171 60 , , PUNCT bibechana-46416 171 61 a. a. PROPN bibechana-46416 171 62 n. n. PROPN bibechana-46416 171 63 ikot ikot PROPN bibechana-46416 171 64 , , PUNCT bibechana-46416 171 65 m. m. PROPN bibechana-46416 171 66 c. c. PROPN bibechana-46416 171 67 onyeaju onyeaju PROPN bibechana-46416 171 68 , , PUNCT bibechana-46416 171 69 and and CCONJ bibechana-46416 171 70 e. e. PROPN bibechana-46416 171 71 o. o. PROPN bibechana-46416 171 72 chukwuocha chukwuocha PROPN bibechana-46416 171 73 , , PUNCT bibechana-46416 171 74 thermodynamic thermodynamic ADJ bibechana-46416 171 75 properties property NOUN bibechana-46416 171 76 of of ADP bibechana-46416 171 77 the the DET bibechana-46416 171 78 modified modify VERB bibechana-46416 171 79 yukawa yukawa PROPN bibechana-46416 171 80 potential potential NOUN bibechana-46416 171 81 , , PUNCT bibechana-46416 171 82 journal journal NOUN bibechana-46416 171 83 of of ADP bibechana-46416 171 84 the the DET bibechana-46416 171 85 korean korean ADJ bibechana-46416 171 86 physical physical ADJ bibechana-46416 171 87 society society NOUN bibechana-46416 171 88 , , PUNCT bibechana-46416 171 89 73(9)(2018)1211 73(9)(2018)1211 NUM bibechana-46416 171 90 - - SYM bibechana-46416 171 91 1218 1218 NUM bibechana-46416 171 92 . . PUNCT bibechana-46416 172 1 [ [ X bibechana-46416 172 2 9 9 NUM bibechana-46416 172 3 ] ] PUNCT bibechana-46416 172 4 e. e. PROPN bibechana-46416 172 5 w. w. PROPN bibechana-46416 172 6 ng ng PROPN bibechana-46416 172 7 and and CCONJ bibechana-46416 172 8 m. m. PROPN bibechana-46416 172 9 geller geller PROPN bibechana-46416 172 10 , , PUNCT bibechana-46416 172 11 a a DET bibechana-46416 172 12 table table NOUN bibechana-46416 172 13 of of ADP bibechana-46416 172 14 integrals integral NOUN bibechana-46416 172 15 of of ADP bibechana-46416 172 16 the the DET bibechana-46416 172 17 error error NOUN bibechana-46416 172 18 functions function NOUN bibechana-46416 172 19 , , PUNCT bibechana-46416 172 20 journal journal NOUN bibechana-46416 172 21 of of ADP bibechana-46416 172 22 research research NOUN bibechana-46416 172 23 of of ADP bibechana-46416 172 24 the the DET bibechana-46416 172 25 national national PROPN bibechana-46416 172 26 bureau bureau PROPN bibechana-46416 172 27 of of ADP bibechana-46416 172 28 standards standards PROPN bibechana-46416 172 29 b. b. 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PUNCT bibechana-46416 172 37 http://www.scielo.org.mx/pdf/rmf/v65n4/0035-001x-rmf-65-04-333.pdf http://www.scielo.org.mx/pdf/rmf/v65n4/0035-001x-rmf-65-04-333.pdf PROPN bibechana-46416 172 38 http://www.scielo.org.mx/pdf/rmf/v65n4/0035-001x-rmf-65-04-333.pdf http://www.scielo.org.mx/pdf/rmf/v65n4/0035-001x-rmf-65-04-333.pdf PROPN bibechana-46416 173 1 https://doi.org/10.1155/2017/9671816 https://doi.org/10.1155/2017/9671816 PROPN bibechana-46416 173 2 https://arxiv.org/pdf/1812.06383.pdf https://arxiv.org/pdf/1812.06383.pdf PROPN bibechana-46416 173 3 https://arxiv.org/ftp/arxiv/papers/2001/2001.04799.pdf https://arxiv.org/ftp/arxiv/papers/2001/2001.04799.pdf PROPN bibechana-46416 173 4 https://doi.org/10.1186/s42787-019-0014-0 https://doi.org/10.1186/s42787-019-0014-0 NUM