id sid tid token lemma pos ap-4339 1 1 acta acta PROPN ap-4339 1 2 polytechnica polytechnica PROPN ap-4339 1 3 doi:10.14311 doi:10.14311 PROPN ap-4339 1 4 / / SYM ap-4339 1 5 ap.2017.57.0391 ap.2017.57.0391 PROPN ap-4339 1 6 acta acta PROPN ap-4339 1 7 polytechnica polytechnica PROPN ap-4339 1 8 57(6):391–398 57(6):391–398 PROPN ap-4339 1 9 , , PUNCT ap-4339 1 10 2017 2017 NUM ap-4339 1 11 © © PROPN ap-4339 1 12 czech czech PROPN ap-4339 1 13 technical technical PROPN ap-4339 1 14 university university PROPN ap-4339 1 15 in in ADP ap-4339 1 16 prague prague PROPN ap-4339 1 17 , , PUNCT ap-4339 1 18 2017 2017 NUM ap-4339 1 19 available available ADJ ap-4339 1 20 online online ADV ap-4339 1 21 at at ADP ap-4339 1 22 http://ojs.cvut.cz/ojs/index.php/ap http://ojs.cvut.cz/ojs/index.php/ap PROPN ap-4339 1 23 highly highly ADV ap-4339 1 24 accurate accurate ADJ ap-4339 1 25 calculation calculation NOUN ap-4339 1 26 of of ADP ap-4339 1 27 the the DET ap-4339 1 28 real real ADJ ap-4339 1 29 and and CCONJ ap-4339 1 30 complex complex ADJ ap-4339 1 31 eigenvalues eigenvalue NOUN ap-4339 1 32 of of ADP ap-4339 1 33 one one NUM ap-4339 1 34 - - PUNCT ap-4339 1 35 dimensional dimensional ADJ ap-4339 1 36 anharmonic anharmonic ADJ ap-4339 1 37 oscillators oscillator NOUN ap-4339 1 38 francisco francisco PROPN ap-4339 1 39 marcelo marcelo PROPN ap-4339 1 40 fernández∗ fernández∗ PROPN ap-4339 1 41 , , PUNCT ap-4339 1 42 javier javier PROPN ap-4339 1 43 garcia garcia PROPN ap-4339 1 44 inifta inifta PROPN ap-4339 1 45 ( ( PUNCT ap-4339 1 46 unlp unlp ADJ ap-4339 1 47 , , PUNCT ap-4339 1 48 cct cct PROPN ap-4339 1 49 la la PROPN ap-4339 1 50 plata plata PROPN ap-4339 1 51 - - PUNCT ap-4339 1 52 conicet conicet NOUN ap-4339 1 53 ) ) PUNCT ap-4339 1 54 , , PUNCT ap-4339 1 55 blvd blvd NOUN ap-4339 1 56 . . PUNCT ap-4339 2 1 113 113 NUM ap-4339 2 2 s s NOUN ap-4339 2 3 / / SYM ap-4339 2 4 n n CCONJ ap-4339 2 5 , , PUNCT ap-4339 2 6 sucursal sucursal ADJ ap-4339 2 7 4 4 NUM ap-4339 2 8 , , PUNCT ap-4339 2 9 casilla casilla X ap-4339 2 10 de de X ap-4339 2 11 correo correo PROPN ap-4339 2 12 16 16 NUM ap-4339 2 13 , , PUNCT ap-4339 2 14 1900 1900 NUM ap-4339 2 15 la la PROPN ap-4339 2 16 plata plata PROPN ap-4339 2 17 , , PUNCT ap-4339 2 18 argentina argentina PROPN ap-4339 2 19 ∗ ∗ PROPN ap-4339 2 20 corresponding correspond VERB ap-4339 2 21 author author NOUN ap-4339 2 22 : : PUNCT ap-4339 2 23 fernande@quimica.unlp.edu.ar fernande@quimica.unlp.edu.ar VERB ap-4339 2 24 abstract abstract ADJ ap-4339 2 25 . . PUNCT ap-4339 3 1 we we PRON ap-4339 3 2 draw draw VERB ap-4339 3 3 attention attention NOUN ap-4339 3 4 on on ADP ap-4339 3 5 the the DET ap-4339 3 6 fact fact NOUN ap-4339 3 7 that that SCONJ ap-4339 3 8 the the DET ap-4339 3 9 riccati riccati NOUN ap-4339 3 10 - - PUNCT ap-4339 3 11 padé padé NOUN ap-4339 3 12 method method NOUN ap-4339 3 13 developed develop VERB ap-4339 3 14 some some DET ap-4339 3 15 time time NOUN ap-4339 3 16 ago ago ADV ap-4339 3 17 enables enable VERB ap-4339 3 18 the the DET ap-4339 3 19 accurate accurate ADJ ap-4339 3 20 calculation calculation NOUN ap-4339 3 21 of of ADP ap-4339 3 22 bound bind VERB ap-4339 3 23 - - PUNCT ap-4339 3 24 state state NOUN ap-4339 3 25 eigenvalues eigenvalue NOUN ap-4339 3 26 as as ADV ap-4339 3 27 well well ADV ap-4339 3 28 as as ADP ap-4339 3 29 of of ADP ap-4339 3 30 resonances resonance NOUN ap-4339 3 31 embedded embed VERB ap-4339 3 32 either either CCONJ ap-4339 3 33 in in ADP ap-4339 3 34 the the DET ap-4339 3 35 continuum continuum ADJ ap-4339 3 36 or or CCONJ ap-4339 3 37 in in ADP ap-4339 3 38 the the DET ap-4339 3 39 discrete discrete ADJ ap-4339 3 40 spectrum spectrum NOUN ap-4339 3 41 . . PUNCT ap-4339 4 1 we we PRON ap-4339 4 2 apply apply VERB ap-4339 4 3 the the DET ap-4339 4 4 approach approach NOUN ap-4339 4 5 to to ADP ap-4339 4 6 several several ADJ ap-4339 4 7 one one NUM ap-4339 4 8 - - PUNCT ap-4339 4 9 dimensional dimensional ADJ ap-4339 4 10 models model NOUN ap-4339 4 11 that that PRON ap-4339 4 12 exhibit exhibit VERB ap-4339 4 13 different different ADJ ap-4339 4 14 kind kind NOUN ap-4339 4 15 of of ADP ap-4339 4 16 spectra spectra NOUN ap-4339 4 17 . . PUNCT ap-4339 5 1 in in ADP ap-4339 5 2 particular particular ADJ ap-4339 5 3 we we PRON ap-4339 5 4 test test VERB ap-4339 5 5 a a DET ap-4339 5 6 wkb wkb NOUN ap-4339 5 7 formula formula NOUN ap-4339 5 8 for for ADP ap-4339 5 9 the the DET ap-4339 5 10 imaginary imaginary ADJ ap-4339 5 11 part part NOUN ap-4339 5 12 of of ADP ap-4339 5 13 the the DET ap-4339 5 14 resonance resonance NOUN ap-4339 5 15 in in ADP ap-4339 5 16 the the DET ap-4339 5 17 discrete discrete ADJ ap-4339 5 18 spectrum spectrum NOUN ap-4339 5 19 of of ADP ap-4339 5 20 a a DET ap-4339 5 21 three three NUM ap-4339 5 22 - - PUNCT ap-4339 5 23 well well NOUN ap-4339 5 24 potential potential NOUN ap-4339 5 25 . . PUNCT ap-4339 6 1 keywords keyword NOUN ap-4339 6 2 : : PUNCT ap-4339 6 3 anharmonic anharmonic ADJ ap-4339 6 4 oscillators oscillator NOUN ap-4339 6 5 ; ; PUNCT ap-4339 6 6 bound bind VERB ap-4339 6 7 states state NOUN ap-4339 6 8 ; ; PUNCT ap-4339 6 9 resonances resonance NOUN ap-4339 6 10 ; ; PUNCT ap-4339 6 11 riccati riccati NOUN ap-4339 6 12 - - PUNCT ap-4339 6 13 padé padé PROPN ap-4339 6 14 method method NOUN ap-4339 6 15 ; ; PUNCT ap-4339 6 16 wkb wkb VERB ap-4339 6 17 asymptotic asymptotic ADJ ap-4339 6 18 expression expression NOUN ap-4339 6 19 . . PUNCT ap-4339 7 1 1 1 X ap-4339 7 2 . . X ap-4339 7 3 introduction introduction NOUN ap-4339 7 4 in in ADP ap-4339 7 5 a a DET ap-4339 7 6 recent recent ADJ ap-4339 7 7 paper paper NOUN ap-4339 7 8 gaudreau gaudreau NOUN ap-4339 7 9 et et NOUN ap-4339 7 10 al[1 al[1 PROPN ap-4339 7 11 ] ] PUNCT ap-4339 7 12 proposed propose VERB ap-4339 7 13 a a DET ap-4339 7 14 method method NOUN ap-4339 7 15 for for ADP ap-4339 7 16 the the DET ap-4339 7 17 calculation calculation NOUN ap-4339 7 18 of of ADP ap-4339 7 19 the the DET ap-4339 7 20 eigenvalues eigenvalue NOUN ap-4339 7 21 of of ADP ap-4339 7 22 the the DET ap-4339 7 23 schrödinger schrödinger ADJ ap-4339 7 24 equation equation NOUN ap-4339 7 25 for for ADP ap-4339 7 26 one one NUM ap-4339 7 27 - - PUNCT ap-4339 7 28 dimensional dimensional ADJ ap-4339 7 29 anharmonic anharmonic ADJ ap-4339 7 30 oscillators oscillator NOUN ap-4339 7 31 . . PUNCT ap-4339 8 1 in in ADP ap-4339 8 2 their their PRON ap-4339 8 3 analysis analysis NOUN ap-4339 8 4 of of ADP ap-4339 8 5 some some PRON ap-4339 8 6 of of ADP ap-4339 8 7 the the DET ap-4339 8 8 many many ADJ ap-4339 8 9 approaches approach NOUN ap-4339 8 10 proposed propose VERB ap-4339 8 11 earlier early ADV ap-4339 8 12 with with ADP ap-4339 8 13 that that DET ap-4339 8 14 purpose purpose NOUN ap-4339 8 15 they they PRON ap-4339 8 16 resorted resort VERB ap-4339 8 17 to to ADP ap-4339 8 18 expressions expression NOUN ap-4339 8 19 of of ADP ap-4339 8 20 the the DET ap-4339 8 21 form form NOUN ap-4339 8 22 : : PUNCT ap-4339 8 23 “ " PUNCT ap-4339 8 24 however however ADV ap-4339 8 25 , , PUNCT ap-4339 8 26 the the DET ap-4339 8 27 existing exist VERB ap-4339 8 28 numerical numerical ADJ ap-4339 8 29 methods method NOUN ap-4339 8 30 are be AUX ap-4339 8 31 mostly mostly ADV ap-4339 8 32 case case NOUN ap-4339 8 33 specific specific ADJ ap-4339 8 34 and and CCONJ ap-4339 8 35 lack lack NOUN ap-4339 8 36 uniformity uniformity NOUN ap-4339 8 37 when when SCONJ ap-4339 8 38 faced face VERB ap-4339 8 39 with with ADP ap-4339 8 40 a a DET ap-4339 8 41 general general ADJ ap-4339 8 42 problem problem NOUN ap-4339 8 43 . . PUNCT ap-4339 8 44 ” " PUNCT ap-4339 9 1 “ " PUNCT ap-4339 9 2 as as SCONJ ap-4339 9 3 can can AUX ap-4339 9 4 be be AUX ap-4339 9 5 seen see VERB ap-4339 9 6 by by ADP ap-4339 9 7 the the DET ap-4339 9 8 numerous numerous ADJ ap-4339 9 9 approaches approach NOUN ap-4339 9 10 which which PRON ap-4339 9 11 have have AUX ap-4339 9 12 been be AUX ap-4339 9 13 developed develop VERB ap-4339 9 14 to to PART ap-4339 9 15 solve solve VERB ap-4339 9 16 this this DET ap-4339 9 17 problem problem NOUN ap-4339 9 18 , , PUNCT ap-4339 9 19 there there PRON ap-4339 9 20 is be VERB ap-4339 9 21 a a DET ap-4339 9 22 beautiful beautiful ADJ ap-4339 9 23 diversity diversity NOUN ap-4339 9 24 yet yet ADV ap-4339 9 25 lack lack NOUN ap-4339 9 26 of of ADP ap-4339 9 27 uniformity uniformity NOUN ap-4339 9 28 in in ADP ap-4339 9 29 its its PRON ap-4339 9 30 resolution resolution NOUN ap-4339 9 31 . . PUNCT ap-4339 10 1 while while SCONJ ap-4339 10 2 several several ADJ ap-4339 10 3 of of ADP ap-4339 10 4 these these DET ap-4339 10 5 methods method NOUN ap-4339 10 6 yield yield VERB ap-4339 10 7 excellent excellent ADJ ap-4339 10 8 results result NOUN ap-4339 10 9 for for ADP ap-4339 10 10 specific specific ADJ ap-4339 10 11 cases case NOUN ap-4339 10 12 , , PUNCT ap-4339 10 13 it it PRON ap-4339 10 14 would would AUX ap-4339 10 15 be be AUX ap-4339 10 16 favorable favorable ADJ ap-4339 10 17 to to PART ap-4339 10 18 have have VERB ap-4339 10 19 one one NUM ap-4339 10 20 general general ADJ ap-4339 10 21 method method NOUN ap-4339 10 22 that that PRON ap-4339 10 23 could could AUX ap-4339 10 24 handle handle VERB ap-4339 10 25 any any DET ap-4339 10 26 anharmonic anharmonic ADJ ap-4339 10 27 potential potential NOUN ap-4339 10 28 while while SCONJ ap-4339 10 29 being be AUX ap-4339 10 30 capable capable ADJ ap-4339 10 31 of of ADP ap-4339 10 32 computing compute VERB ap-4339 10 33 efficiently efficiently ADJ ap-4339 10 34 approximations approximation NOUN ap-4339 10 35 of of ADP ap-4339 10 36 eigenvalues eigenvalue NOUN ap-4339 10 37 to to ADP ap-4339 10 38 a a DET ap-4339 10 39 high high ADJ ap-4339 10 40 pre pre ADJ ap-4339 10 41 - - ADJ ap-4339 10 42 determined determined ADJ ap-4339 10 43 accuracy accuracy NOUN ap-4339 10 44 . . PUNCT ap-4339 10 45 ” " PUNCT ap-4339 11 1 “ " PUNCT ap-4339 11 2 various various ADJ ap-4339 11 3 methods method NOUN ap-4339 11 4 have have AUX ap-4339 11 5 been be AUX ap-4339 11 6 used use VERB ap-4339 11 7 to to PART ap-4339 11 8 calculate calculate VERB ap-4339 11 9 the the DET ap-4339 11 10 energy energy NOUN ap-4339 11 11 eigenvalues eigenvalue NOUN ap-4339 11 12 of of ADP ap-4339 11 13 quantum quantum NOUN ap-4339 11 14 anharmonic anharmonic ADJ ap-4339 11 15 oscillators oscillator NOUN ap-4339 11 16 given give VERB ap-4339 11 17 a a DET ap-4339 11 18 specific specific ADJ ap-4339 11 19 set set NOUN ap-4339 11 20 of of ADP ap-4339 11 21 parameters parameter NOUN ap-4339 11 22 . . PUNCT ap-4339 12 1 while while SCONJ ap-4339 12 2 several several ADJ ap-4339 12 3 of of ADP ap-4339 12 4 these these DET ap-4339 12 5 methods method NOUN ap-4339 12 6 yield yield VERB ap-4339 12 7 excellent excellent ADJ ap-4339 12 8 results result NOUN ap-4339 12 9 for for ADP ap-4339 12 10 specific specific ADJ ap-4339 12 11 cases case NOUN ap-4339 12 12 , , PUNCT ap-4339 12 13 there there PRON ap-4339 12 14 is be VERB ap-4339 12 15 a a DET ap-4339 12 16 beautiful beautiful ADJ ap-4339 12 17 diversity diversity NOUN ap-4339 12 18 yet yet ADV ap-4339 12 19 lack lack NOUN ap-4339 12 20 of of ADP ap-4339 12 21 uniformity uniformity NOUN ap-4339 12 22 in in ADP ap-4339 12 23 the the DET ap-4339 12 24 resolution resolution NOUN ap-4339 12 25 of of ADP ap-4339 12 26 this this DET ap-4339 12 27 problem problem NOUN ap-4339 12 28 . . PUNCT ap-4339 12 29 ” " PUNCT ap-4339 13 1 the the DET ap-4339 13 2 authors author NOUN ap-4339 13 3 put put VERB ap-4339 13 4 forward forward ADP ap-4339 13 5 an an DET ap-4339 13 6 approach approach NOUN ap-4339 13 7 that that PRON ap-4339 13 8 they they PRON ap-4339 13 9 termed term VERB ap-4339 13 10 double double ADJ ap-4339 13 11 exponential exponential ADJ ap-4339 13 12 sinc sinc NOUN ap-4339 13 13 collocation collocation NOUN ap-4339 13 14 method method NOUN ap-4339 13 15 ( ( PUNCT ap-4339 13 16 descm descm PROPN ap-4339 13 17 ) ) PUNCT ap-4339 13 18 and and CCONJ ap-4339 13 19 reported report VERB ap-4339 13 20 results result NOUN ap-4339 13 21 of of ADP ap-4339 13 22 remarkable remarkable ADJ ap-4339 13 23 accuracy accuracy NOUN ap-4339 13 24 for for ADP ap-4339 13 25 a a DET ap-4339 13 26 wide wide ADJ ap-4339 13 27 variety variety NOUN ap-4339 13 28 of of ADP ap-4339 13 29 problems problem NOUN ap-4339 13 30 . . PUNCT ap-4339 14 1 in in ADP ap-4339 14 2 fact fact NOUN ap-4339 14 3 they they PRON ap-4339 14 4 stated state VERB ap-4339 14 5 that that SCONJ ap-4339 14 6 “ " PUNCT ap-4339 14 7 in in ADP ap-4339 14 8 the the DET ap-4339 14 9 present present ADJ ap-4339 14 10 work work NOUN ap-4339 14 11 , , PUNCT ap-4339 14 12 we we PRON ap-4339 14 13 use use VERB ap-4339 14 14 this this DET ap-4339 14 15 method method NOUN ap-4339 14 16 to to PART ap-4339 14 17 compute compute VERB ap-4339 14 18 energy energy NOUN ap-4339 14 19 eigenvalues eigenvalue NOUN ap-4339 14 20 of of ADP ap-4339 14 21 anharmonic anharmonic ADJ ap-4339 14 22 oscillators oscillator NOUN ap-4339 14 23 to to ADP ap-4339 14 24 unprecedented unprecedented ADJ ap-4339 14 25 accuracy accuracy NOUN ap-4339 14 26 ” " PUNCT ap-4339 14 27 which which PRON ap-4339 14 28 may may AUX ap-4339 14 29 perhaps perhaps ADV ap-4339 14 30 be be AUX ap-4339 14 31 true true ADJ ap-4339 14 32 for for ADP ap-4339 14 33 some some PRON ap-4339 14 34 of of ADP ap-4339 14 35 the the DET ap-4339 14 36 models model NOUN ap-4339 14 37 chosen choose VERB ap-4339 14 38 but but CCONJ ap-4339 14 39 not not PART ap-4339 14 40 for for ADP ap-4339 14 41 other other ADJ ap-4339 14 42 similar similar ADJ ap-4339 14 43 examples example NOUN ap-4339 14 44 . . PUNCT ap-4339 15 1 for for ADP ap-4339 15 2 example example NOUN ap-4339 15 3 , , PUNCT ap-4339 15 4 in in ADP ap-4339 15 5 an an DET ap-4339 15 6 unpublished unpublished ADJ ap-4339 15 7 article article NOUN ap-4339 15 8 trott[2 trott[2 X ap-4339 15 9 ] ] PUNCT ap-4339 15 10 obtained obtain VERB ap-4339 15 11 the the DET ap-4339 15 12 ground ground NOUN ap-4339 15 13 - - PUNCT ap-4339 15 14 state state NOUN ap-4339 15 15 energy energy NOUN ap-4339 15 16 of of ADP ap-4339 15 17 the the DET ap-4339 15 18 anharmonic anharmonic ADJ ap-4339 15 19 oscillator oscillator NOUN ap-4339 15 20 with with ADP ap-4339 15 21 potential potential ADJ ap-4339 15 22 v v NOUN ap-4339 15 23 ( ( PUNCT ap-4339 15 24 x x NOUN ap-4339 15 25 ) ) PUNCT ap-4339 15 26 = = SYM ap-4339 15 27 x4 x4 ADJ ap-4339 15 28 with with ADP ap-4339 15 29 more more ADJ ap-4339 15 30 than than ADP ap-4339 15 31 1000 1000 NUM ap-4339 15 32 accurate accurate ADJ ap-4339 15 33 digits digit NOUN ap-4339 15 34 . . PUNCT ap-4339 16 1 his his PRON ap-4339 16 2 approach approach NOUN ap-4339 16 3 is be AUX ap-4339 16 4 based base VERB ap-4339 16 5 on on ADP ap-4339 16 6 the the DET ap-4339 16 7 straightforward straightforward ADJ ap-4339 16 8 expansion expansion NOUN ap-4339 16 9 of of ADP ap-4339 16 10 the the DET ap-4339 16 11 wavefunction wavefunction NOUN ap-4339 16 12 in in ADP ap-4339 16 13 a a DET ap-4339 16 14 taylor taylor PROPN ap-4339 16 15 series series NOUN ap-4339 16 16 about about ADP ap-4339 16 17 the the DET ap-4339 16 18 origin origin NOUN ap-4339 16 19 . . PUNCT ap-4339 17 1 one one NUM ap-4339 17 2 of of ADP ap-4339 17 3 the the DET ap-4339 17 4 methods method NOUN ap-4339 17 5 mentioned mention VERB ap-4339 17 6 by by ADP ap-4339 17 7 gaudreau gaudreau PROPN ap-4339 17 8 et et PROPN ap-4339 17 9 al[1 al[1 PROPN ap-4339 17 10 ] ] PUNCT ap-4339 17 11 is be AUX ap-4339 17 12 the the DET ap-4339 17 13 riccati riccati NOUN ap-4339 17 14 - - PUNCT ap-4339 17 15 padé padé NOUN ap-4339 17 16 method method NOUN ap-4339 17 17 ( ( PUNCT ap-4339 17 18 rpm rpm PROPN ap-4339 17 19 ) ) PUNCT ap-4339 17 20 based base VERB ap-4339 17 21 on on ADP ap-4339 17 22 a a DET ap-4339 17 23 rational rational ADJ ap-4339 17 24 approximation approximation NOUN ap-4339 17 25 to to ADP ap-4339 17 26 the the DET ap-4339 17 27 logarithmic logarithmic ADJ ap-4339 17 28 derivative derivative NOUN ap-4339 17 29 of of ADP ap-4339 17 30 the the DET ap-4339 17 31 wavefunction wavefunction NOUN ap-4339 17 32 that that PRON ap-4339 17 33 satisfies satisfy VERB ap-4339 17 34 a a DET ap-4339 17 35 well well ADV ap-4339 17 36 known know VERB ap-4339 17 37 riccati riccati PROPN ap-4339 17 38 equation[3 equation[3 PROPN ap-4339 17 39 , , PUNCT ap-4339 17 40 4 4 NUM ap-4339 17 41 ] ] PUNCT ap-4339 17 42 . . PUNCT ap-4339 18 1 in in ADP ap-4339 18 2 their their PRON ap-4339 18 3 brief brief ADJ ap-4339 18 4 analysis analysis NOUN ap-4339 18 5 of of ADP ap-4339 18 6 the the DET ap-4339 18 7 rpm rpm NOUN ap-4339 18 8 the the DET ap-4339 18 9 authors author NOUN ap-4339 18 10 did do AUX ap-4339 18 11 not not PART ap-4339 18 12 mention mention VERB ap-4339 18 13 that that SCONJ ap-4339 18 14 this this DET ap-4339 18 15 approach approach NOUN ap-4339 18 16 not not PART ap-4339 18 17 only only ADV ap-4339 18 18 yields yield VERB ap-4339 18 19 the the DET ap-4339 18 20 bound bind VERB ap-4339 18 21 - - PUNCT ap-4339 18 22 state state NOUN ap-4339 18 23 eigenvalues eigenvalue NOUN ap-4339 18 24 but but CCONJ ap-4339 18 25 also also ADV ap-4339 18 26 the the DET ap-4339 18 27 resonances resonance NOUN ap-4339 18 28 embedded embed VERB ap-4339 18 29 in in ADP ap-4339 18 30 the the DET ap-4339 18 31 continuum[5 continuum[5 NOUN ap-4339 18 32 ] ] PUNCT ap-4339 18 33 . . PUNCT ap-4339 19 1 what what PRON ap-4339 19 2 is be AUX ap-4339 19 3 more more ADJ ap-4339 19 4 , , PUNCT ap-4339 19 5 the the DET ap-4339 19 6 same same ADJ ap-4339 19 7 rpm rpm ADJ ap-4339 19 8 quantization quantization NOUN ap-4339 19 9 condition condition NOUN ap-4339 19 10 , , PUNCT ap-4339 19 11 given give VERB ap-4339 19 12 by by ADP ap-4339 19 13 a a DET ap-4339 19 14 hankel hankel NOUN ap-4339 19 15 determinant determinant ADJ ap-4339 19 16 , , PUNCT ap-4339 19 17 produces produce VERB ap-4339 19 18 the the DET ap-4339 19 19 bound bind VERB ap-4339 19 20 - - PUNCT ap-4339 19 21 state state NOUN ap-4339 19 22 eigenvalues eigenvalue NOUN ap-4339 19 23 , , PUNCT ap-4339 19 24 the the DET ap-4339 19 25 resonances resonance NOUN ap-4339 19 26 embedded embed VERB ap-4339 19 27 in in ADP ap-4339 19 28 the the DET ap-4339 19 29 continuum continuum NOUN ap-4339 19 30 as as ADV ap-4339 19 31 well well ADV ap-4339 19 32 as as ADP ap-4339 19 33 some some DET ap-4339 19 34 kind kind NOUN ap-4339 19 35 of of ADP ap-4339 19 36 strange strange ADJ ap-4339 19 37 resonances resonance NOUN ap-4339 19 38 located locate VERB ap-4339 19 39 in in ADP ap-4339 19 40 the the DET ap-4339 19 41 discrete discrete ADJ ap-4339 19 42 spectrum spectrum NOUN ap-4339 19 43 of of ADP ap-4339 19 44 some some DET ap-4339 19 45 multiple multiple ADJ ap-4339 19 46 - - PUNCT ap-4339 19 47 well well NOUN ap-4339 19 48 oscillators[6 oscillators[6 NOUN ap-4339 19 49 ] ] PUNCT ap-4339 19 50 . . PUNCT ap-4339 20 1 it it PRON ap-4339 20 2 is be AUX ap-4339 20 3 not not PART ap-4339 20 4 clear clear ADJ ap-4339 20 5 from from ADP ap-4339 20 6 the the DET ap-4339 20 7 content content NOUN ap-4339 20 8 of[1 of[1 X ap-4339 20 9 ] ] PUNCT ap-4339 20 10 whether whether SCONJ ap-4339 20 11 the the DET ap-4339 20 12 descm descm NOUN ap-4339 20 13 is be AUX ap-4339 20 14 also also ADV ap-4339 20 15 suitable suitable ADJ ap-4339 20 16 for for ADP ap-4339 20 17 the the DET ap-4339 20 18 calculation calculation NOUN ap-4339 20 19 of of ADP ap-4339 20 20 such such ADJ ap-4339 20 21 complex complex ADJ ap-4339 20 22 eigenvalues eigenvalue NOUN ap-4339 20 23 . . PUNCT ap-4339 21 1 the the DET ap-4339 21 2 accuracy accuracy NOUN ap-4339 21 3 of of ADP ap-4339 21 4 the the DET ap-4339 21 5 calculated calculate VERB ap-4339 21 6 eigenvalues eigenvalue NOUN ap-4339 21 7 not not PART ap-4339 21 8 only only ADV ap-4339 21 9 depends depend VERB ap-4339 21 10 on on ADP ap-4339 21 11 the the DET ap-4339 21 12 chosen choose VERB ap-4339 21 13 method method NOUN ap-4339 21 14 but but CCONJ ap-4339 21 15 also also ADV ap-4339 21 16 on on ADP ap-4339 21 17 the the DET ap-4339 21 18 available available ADJ ap-4339 21 19 computation computation NOUN ap-4339 21 20 facilities facility NOUN ap-4339 21 21 and and CCONJ ap-4339 21 22 on on ADP ap-4339 21 23 the the DET ap-4339 21 24 art art NOUN ap-4339 21 25 of of ADP ap-4339 21 26 programming programming NOUN ap-4339 21 27 . . PUNCT ap-4339 22 1 for for ADP ap-4339 22 2 this this DET ap-4339 22 3 reason reason NOUN ap-4339 22 4 the the DET ap-4339 22 5 comparison comparison NOUN ap-4339 22 6 of of ADP ap-4339 22 7 the the DET ap-4339 22 8 accuracy accuracy NOUN ap-4339 22 9 of of ADP ap-4339 22 10 the the DET ap-4339 22 11 results result NOUN ap-4339 22 12 reported report VERB ap-4339 22 13 in in ADP ap-4339 22 14 a a DET ap-4339 22 15 number number NOUN ap-4339 22 16 of of ADP ap-4339 22 17 papers paper NOUN ap-4339 22 18 spread spread VERB ap-4339 22 19 in in ADP ap-4339 22 20 time time NOUN ap-4339 22 21 should should AUX ap-4339 22 22 be be AUX ap-4339 22 23 carried carry VERB ap-4339 22 24 out out ADP ap-4339 22 25 with with ADP ap-4339 22 26 care care NOUN ap-4339 22 27 . . PUNCT ap-4339 23 1 the the DET ap-4339 23 2 purpose purpose NOUN ap-4339 23 3 of of ADP ap-4339 23 4 this this DET ap-4339 23 5 paper paper NOUN ap-4339 23 6 is be AUX ap-4339 23 7 two two NUM ap-4339 23 8 - - NUM ap-4339 23 9 fold fold ADJ ap-4339 23 10 . . PUNCT ap-4339 24 1 first first ADV ap-4339 24 2 , , PUNCT ap-4339 24 3 we we PRON ap-4339 24 4 show show VERB ap-4339 24 5 that that SCONJ ap-4339 24 6 the the DET ap-4339 24 7 rpm rpm NOUN ap-4339 24 8 can can AUX ap-4339 24 9 in in ADP ap-4339 24 10 fact fact NOUN ap-4339 24 11 yield yield VERB ap-4339 24 12 extremely extremely ADV ap-4339 24 13 accurate accurate ADJ ap-4339 24 14 eigenvalues eigenvalue NOUN ap-4339 24 15 because because SCONJ ap-4339 24 16 it it PRON ap-4339 24 17 exhibits exhibit VERB ap-4339 24 18 exponential exponential ADJ ap-4339 24 19 convergence convergence NOUN ap-4339 24 20 . . PUNCT ap-4339 25 1 to to ADP ap-4339 25 2 that that DET ap-4339 25 3 end end NOUN ap-4339 25 4 it it PRON ap-4339 25 5 is be AUX ap-4339 25 6 only only ADV ap-4339 25 7 necessary necessary ADJ ap-4339 25 8 to to PART ap-4339 25 9 program program VERB ap-4339 25 10 the the DET ap-4339 25 11 quantization quantization NOUN ap-4339 25 12 condition condition NOUN ap-4339 25 13 in in ADP ap-4339 25 14 an an DET ap-4339 25 15 efficient efficient ADJ ap-4339 25 16 way way NOUN ap-4339 25 17 in in ADP ap-4339 25 18 a a DET ap-4339 25 19 convenient convenient ADJ ap-4339 25 20 platform platform NOUN ap-4339 25 21 . . PUNCT ap-4339 26 1 second second ADJ ap-4339 26 2 , , PUNCT ap-4339 26 3 we we PRON ap-4339 26 4 stress stress VERB ap-4339 26 5 the the DET ap-4339 26 6 fact fact NOUN ap-4339 26 7 that that SCONJ ap-4339 26 8 the the DET ap-4339 26 9 rpm rpm NOUN ap-4339 26 10 yields yield NOUN ap-4339 26 11 both both CCONJ ap-4339 26 12 real real ADJ ap-4339 26 13 and and CCONJ ap-4339 26 14 complex complex ADJ ap-4339 26 15 eigenvalues eigenvalue NOUN ap-4339 26 16 with with ADP ap-4339 26 17 similar similar ADJ ap-4339 26 18 accuracy accuracy NOUN ap-4339 26 19 through through ADP ap-4339 26 20 the the DET ap-4339 26 21 same same ADJ ap-4339 26 22 quantization quantization NOUN ap-4339 26 23 condition condition NOUN ap-4339 26 24 . . PUNCT ap-4339 27 1 more more ADV ap-4339 27 2 precisely precisely ADV ap-4339 27 3 : : PUNCT ap-4339 27 4 it it PRON ap-4339 27 5 is be AUX ap-4339 27 6 not not PART ap-4339 27 7 necessary necessary ADJ ap-4339 27 8 to to PART ap-4339 27 9 modify modify VERB ap-4339 27 10 the the DET ap-4339 27 11 algorithm algorithm NOUN ap-4339 27 12 in in ADP ap-4339 27 13 order order NOUN ap-4339 27 14 to to PART ap-4339 27 15 obtain obtain VERB ap-4339 27 16 such such ADJ ap-4339 27 17 apparently apparently ADV ap-4339 27 18 dissimilar dissimilar ADJ ap-4339 27 19 types type NOUN ap-4339 27 20 of of ADP ap-4339 27 21 eigenvalues eigenvalue NOUN ap-4339 27 22 that that PRON ap-4339 27 23 are be AUX ap-4339 27 24 associated associate VERB ap-4339 27 25 to to ADP ap-4339 27 26 different different ADJ ap-4339 27 27 boundary boundary ADJ ap-4339 27 28 conditions condition NOUN ap-4339 27 29 of of ADP ap-4339 27 30 the the DET ap-4339 27 31 eigensolution eigensolution NOUN ap-4339 27 32 . . PUNCT ap-4339 28 1 in in ADP ap-4339 28 2 section section NOUN ap-4339 28 3 2 2 NUM ap-4339 28 4 we we PRON ap-4339 28 5 outline outline VERB ap-4339 28 6 the the DET ap-4339 28 7 rpm rpm NOUN ap-4339 28 8 for for ADP ap-4339 28 9 even even ADJ ap-4339 28 10 - - PUNCT ap-4339 28 11 parity parity NOUN ap-4339 28 12 potentials potential NOUN ap-4339 28 13 . . PUNCT ap-4339 29 1 in in ADP ap-4339 29 2 section section NOUN ap-4339 29 3 3 3 NUM ap-4339 29 4 we we PRON ap-4339 29 5 apply apply VERB ap-4339 29 6 this this DET ap-4339 29 7 approach approach NOUN ap-4339 29 8 to to ADP ap-4339 29 9 some some PRON ap-4339 29 10 of of ADP ap-4339 29 11 the the DET ap-4339 29 12 examples example NOUN ap-4339 29 13 discussed discuss VERB ap-4339 29 14 by by ADP ap-4339 29 15 gaudreau gaudreau PROPN ap-4339 29 16 et et NOUN ap-4339 29 17 al[1 al[1 PROPN ap-4339 29 18 ] ] PUNCT ap-4339 29 19 and and CCONJ ap-4339 29 20 obtain obtain VERB ap-4339 29 21 eigenvalues eigenvalue NOUN ap-4339 29 22 with with ADP ap-4339 29 23 remarkable remarkable ADJ ap-4339 29 24 accuracy accuracy NOUN ap-4339 29 25 . . PUNCT ap-4339 30 1 in in ADP ap-4339 30 2 this this DET ap-4339 30 3 section section NOUN ap-4339 30 4 we we PRON ap-4339 30 5 also also ADV ap-4339 30 6 calculate calculate VERB ap-4339 30 7 several several ADJ ap-4339 30 8 resonances resonance NOUN ap-4339 30 9 supported support VERB ap-4339 30 10 by by ADP ap-4339 30 11 anharmonic anharmonic ADJ ap-4339 30 12 oscillators oscillator NOUN ap-4339 30 13 that that PRON ap-4339 30 14 were be AUX ap-4339 30 15 not not PART ap-4339 30 16 taken take VERB ap-4339 30 17 into into ADP ap-4339 30 18 account account NOUN ap-4339 30 19 by by ADP ap-4339 30 20 those those DET ap-4339 30 21 authors author NOUN ap-4339 30 22 . . PUNCT ap-4339 31 1 391 391 NUM ap-4339 31 2 http://dx.doi.org/10.14311/ap.2017.57.0391 http://dx.doi.org/10.14311/ap.2017.57.0391 ADP ap-4339 31 3 http://ojs.cvut.cz/ojs/index.php/ap http://ojs.cvut.cz/ojs/index.php/ap PROPN ap-4339 31 4 francisco francisco PROPN ap-4339 31 5 marcelo marcelo PROPN ap-4339 31 6 fernández fernández PROPN ap-4339 31 7 , , PUNCT ap-4339 31 8 javier javier PROPN ap-4339 31 9 garcia garcia PROPN ap-4339 31 10 acta acta PROPN ap-4339 31 11 polytechnica polytechnica PROPN ap-4339 31 12 we we PRON ap-4339 31 13 consider consider VERB ap-4339 31 14 examples example NOUN ap-4339 31 15 of of ADP ap-4339 31 16 resonances resonance NOUN ap-4339 31 17 embedded embed VERB ap-4339 31 18 in in ADP ap-4339 31 19 the the DET ap-4339 31 20 continuous continuous ADJ ap-4339 31 21 as as ADV ap-4339 31 22 well well ADV ap-4339 31 23 as as ADP ap-4339 31 24 in in ADP ap-4339 31 25 the the DET ap-4339 31 26 discrete discrete ADJ ap-4339 31 27 spectrum spectrum NOUN ap-4339 31 28 . . PUNCT ap-4339 32 1 finally finally ADV ap-4339 32 2 , , PUNCT ap-4339 32 3 in in ADP ap-4339 32 4 section section NOUN ap-4339 32 5 4 4 NUM ap-4339 32 6 we we PRON ap-4339 32 7 summarize summarize VERB ap-4339 32 8 the the DET ap-4339 32 9 main main ADJ ap-4339 32 10 results result NOUN ap-4339 32 11 and and CCONJ ap-4339 32 12 draw draw VERB ap-4339 32 13 conclusions conclusion NOUN ap-4339 32 14 . . PUNCT ap-4339 33 1 2 2 X ap-4339 33 2 . . X ap-4339 33 3 the the DET ap-4339 33 4 riccati riccati NOUN ap-4339 33 5 - - PUNCT ap-4339 33 6 padé padé NOUN ap-4339 33 7 method method NOUN ap-4339 33 8 the the DET ap-4339 33 9 dimensionless dimensionless NOUN ap-4339 33 10 schrödinger schrödinger ADJ ap-4339 33 11 equation equation NOUN ap-4339 33 12 for for ADP ap-4339 33 13 a a DET ap-4339 33 14 one one NUM ap-4339 33 15 - - PUNCT ap-4339 33 16 dimensional dimensional ADJ ap-4339 33 17 model model NOUN ap-4339 33 18 reads read VERB ap-4339 33 19 ψ′′(x ψ′′(x NOUN ap-4339 33 20 ) ) PUNCT ap-4339 33 21 + + CCONJ ap-4339 34 1 [ [ X ap-4339 34 2 e e X ap-4339 34 3 − − PROPN ap-4339 34 4 v v NOUN ap-4339 34 5 ( ( PUNCT ap-4339 34 6 x)]ψ(x x)]ψ(x PROPN ap-4339 34 7 ) ) PUNCT ap-4339 34 8 = = SYM ap-4339 34 9 0 0 NUM ap-4339 34 10 , , PUNCT ap-4339 34 11 ( ( PUNCT ap-4339 34 12 1 1 X ap-4339 34 13 ) ) PUNCT ap-4339 34 14 where where SCONJ ap-4339 34 15 e e NOUN ap-4339 34 16 is be AUX ap-4339 34 17 the the DET ap-4339 34 18 eigenvalue eigenvalue PROPN ap-4339 34 19 and and CCONJ ap-4339 34 20 ψ(x ψ(x NOUN ap-4339 34 21 ) ) PUNCT ap-4339 34 22 is be AUX ap-4339 34 23 the the DET ap-4339 34 24 eigenfunction eigenfunction NOUN ap-4339 34 25 that that PRON ap-4339 34 26 satisfies satisfy VERB ap-4339 34 27 some some PRON ap-4339 34 28 given give VERB ap-4339 34 29 boundary boundary ADJ ap-4339 34 30 conditions condition NOUN ap-4339 34 31 . . PUNCT ap-4339 35 1 for for ADP ap-4339 35 2 example example NOUN ap-4339 35 3 , , PUNCT ap-4339 35 4 lim lim PROPN ap-4339 35 5 |x|→∞ |x|→∞ NOUN ap-4339 35 6 ψ(x ψ(x PROPN ap-4339 35 7 ) ) PUNCT ap-4339 35 8 = = SYM ap-4339 36 1 0 0 NUM ap-4339 36 2 determines determine VERB ap-4339 36 3 the the DET ap-4339 36 4 discrete discrete ADJ ap-4339 36 5 spectrum spectrum NOUN ap-4339 36 6 and and CCONJ ap-4339 36 7 the the DET ap-4339 36 8 resonances resonance NOUN ap-4339 36 9 are be AUX ap-4339 36 10 associated associate VERB ap-4339 36 11 to to ADP ap-4339 36 12 outgoing outgoing ADJ ap-4339 36 13 waves wave NOUN ap-4339 36 14 in in ADP ap-4339 36 15 each each DET ap-4339 36 16 channel channel NOUN ap-4339 36 17 ( ( PUNCT ap-4339 36 18 for for ADP ap-4339 36 19 example example NOUN ap-4339 36 20 , , PUNCT ap-4339 36 21 ψ(x ψ(x NOUN ap-4339 36 22 ) ) PUNCT ap-4339 36 23 ∼ ∼ NOUN ap-4339 36 24 aeikx aeikx NOUN ap-4339 36 25 ) ) PUNCT ap-4339 36 26 . . PUNCT ap-4339 37 1 in in ADP ap-4339 37 2 this this DET ap-4339 37 3 paper paper NOUN ap-4339 37 4 we we PRON ap-4339 37 5 restrict restrict VERB ap-4339 37 6 ourselves ourselves PRON ap-4339 37 7 to to PART ap-4339 37 8 anharmonic anharmonic VERB ap-4339 37 9 oscillators oscillator NOUN ap-4339 37 10 with with ADP ap-4339 37 11 even even ADJ ap-4339 37 12 - - PUNCT ap-4339 37 13 parity parity NOUN ap-4339 37 14 potentials potential VERB ap-4339 37 15 v v X ap-4339 37 16 ( ( PUNCT ap-4339 37 17 −x −x NOUN ap-4339 37 18 ) ) PUNCT ap-4339 37 19 = = SYM ap-4339 37 20 v v X ap-4339 37 21 ( ( PUNCT ap-4339 37 22 x x NOUN ap-4339 37 23 ) ) PUNCT ap-4339 37 24 to to PART ap-4339 37 25 facilitate facilitate VERB ap-4339 37 26 the the DET ap-4339 37 27 comparison comparison NOUN ap-4339 37 28 with with ADP ap-4339 37 29 the the DET ap-4339 37 30 results result NOUN ap-4339 37 31 reported report VERB ap-4339 37 32 by by ADP ap-4339 37 33 gaudreau gaudreau PROPN ap-4339 37 34 et et NOUN ap-4339 37 35 al[1 al[1 PROPN ap-4339 37 36 ] ] PUNCT ap-4339 37 37 but but CCONJ ap-4339 37 38 it it PRON ap-4339 37 39 should should AUX ap-4339 37 40 be be AUX ap-4339 37 41 taken take VERB ap-4339 37 42 into into ADP ap-4339 37 43 account account NOUN ap-4339 37 44 that that SCONJ ap-4339 37 45 the the DET ap-4339 37 46 approach approach NOUN ap-4339 37 47 applies apply VERB ap-4339 37 48 also also ADV ap-4339 37 49 to to ADP ap-4339 37 50 no no DET ap-4339 37 51 non non ADJ ap-4339 37 52 - - ADJ ap-4339 37 53 symmetric symmetric ADJ ap-4339 37 54 potentials[7 potentials[7 PROPN ap-4339 37 55 ] ] PUNCT ap-4339 37 56 . . PUNCT ap-4339 38 1 in in ADP ap-4339 38 2 order order NOUN ap-4339 38 3 to to PART ap-4339 38 4 apply apply VERB ap-4339 38 5 the the DET ap-4339 38 6 rpm rpm NOUN ap-4339 38 7 we we PRON ap-4339 38 8 define define VERB ap-4339 38 9 the the DET ap-4339 38 10 regularized regularize VERB ap-4339 38 11 logarithmic logarithmic ADJ ap-4339 38 12 derivative derivative NOUN ap-4339 38 13 of of ADP ap-4339 38 14 the the DET ap-4339 38 15 eigenfunction eigenfunction NOUN ap-4339 38 16 f(x f(x PROPN ap-4339 38 17 ) ) PUNCT ap-4339 38 18 = = SYM ap-4339 38 19 s s NOUN ap-4339 38 20 x x X ap-4339 38 21 − − PRON ap-4339 38 22 ψ′(x ψ′(x NUM ap-4339 38 23 ) ) PUNCT ap-4339 38 24 ψ(x ψ(x NOUN ap-4339 38 25 ) ) PUNCT ap-4339 38 26 , , PUNCT ap-4339 38 27 ( ( PUNCT ap-4339 38 28 2 2 X ap-4339 38 29 ) ) PUNCT ap-4339 38 30 that that PRON ap-4339 38 31 satisfies satisfy VERB ap-4339 38 32 the the DET ap-4339 38 33 riccati riccati PROPN ap-4339 38 34 equation equation NOUN ap-4339 38 35 f f PROPN ap-4339 38 36 ′(x ′(x PROPN ap-4339 38 37 ) ) PUNCT ap-4339 38 38 + + NUM ap-4339 39 1 2sf(x 2sf(x X ap-4339 39 2 ) ) PUNCT ap-4339 40 1 x x PUNCT ap-4339 40 2 − − NOUN ap-4339 40 3 f(x)2 f(x)2 NOUN ap-4339 40 4 + + CCONJ ap-4339 40 5 v v X ap-4339 40 6 ( ( PUNCT ap-4339 40 7 x)− x)− PROPN ap-4339 40 8 e e NOUN ap-4339 40 9 = = SYM ap-4339 40 10 0 0 PROPN ap-4339 40 11 , , PUNCT ap-4339 40 12 ( ( PUNCT ap-4339 40 13 3 3 X ap-4339 40 14 ) ) PUNCT ap-4339 40 15 where where SCONJ ap-4339 40 16 s s VERB ap-4339 40 17 = = X ap-4339 40 18 0 0 NUM ap-4339 40 19 or or CCONJ ap-4339 40 20 s s X ap-4339 40 21 = = SYM ap-4339 40 22 1 1 NUM ap-4339 40 23 for for ADP ap-4339 40 24 even even ADV ap-4339 40 25 or or CCONJ ap-4339 40 26 odd odd ADJ ap-4339 40 27 states state NOUN ap-4339 40 28 , , PUNCT ap-4339 40 29 respectively respectively ADV ap-4339 40 30 . . PUNCT ap-4339 41 1 if if SCONJ ap-4339 41 2 v v INTJ ap-4339 41 3 ( ( PUNCT ap-4339 41 4 x x X ap-4339 41 5 ) ) PUNCT ap-4339 41 6 is be AUX ap-4339 41 7 a a DET ap-4339 41 8 polynomial polynomial ADJ ap-4339 41 9 function function NOUN ap-4339 41 10 of of ADP ap-4339 41 11 x x PUNCT ap-4339 41 12 or or CCONJ ap-4339 41 13 it it PRON ap-4339 41 14 can can AUX ap-4339 41 15 be be AUX ap-4339 41 16 expanded expand VERB ap-4339 41 17 in in ADP ap-4339 41 18 a a DET ap-4339 41 19 taylor taylor PROPN ap-4339 41 20 series series NOUN ap-4339 41 21 about about ADP ap-4339 41 22 x x PUNCT ap-4339 42 1 = = SYM ap-4339 42 2 0 0 NUM ap-4339 42 3 then then ADV ap-4339 42 4 one one PRON ap-4339 42 5 can can AUX ap-4339 42 6 also also ADV ap-4339 42 7 expand expand VERB ap-4339 42 8 f(x f(x PROPN ap-4339 42 9 ) ) PUNCT ap-4339 42 10 in in ADP ap-4339 42 11 a a DET ap-4339 42 12 taylor taylor PROPN ap-4339 42 13 series series NOUN ap-4339 42 14 about about ADP ap-4339 42 15 the the DET ap-4339 42 16 origin origin NOUN ap-4339 42 17 f(x f(x PROPN ap-4339 42 18 ) ) PUNCT ap-4339 43 1 = = PUNCT ap-4339 44 1 x x X ap-4339 45 1 ∞∑ ∞∑ NUM ap-4339 45 2 j=0 j=0 ADJ ap-4339 45 3 fj(e)x2j fj(e)x2j X ap-4339 45 4 . . PUNCT ap-4339 46 1 ( ( PUNCT ap-4339 46 2 4 4 X ap-4339 46 3 ) ) PUNCT ap-4339 46 4 on on ADP ap-4339 46 5 arguing argue VERB ap-4339 46 6 as as ADP ap-4339 46 7 in in ADP ap-4339 46 8 earlier early ADJ ap-4339 46 9 papers paper NOUN ap-4339 46 10 we we PRON ap-4339 46 11 conclude conclude VERB ap-4339 46 12 that that SCONJ ap-4339 46 13 we we PRON ap-4339 46 14 can can AUX ap-4339 46 15 obtain obtain VERB ap-4339 46 16 approximate approximate ADJ ap-4339 46 17 eigenvalues eigenvalue NOUN ap-4339 46 18 to to ADP ap-4339 46 19 the the DET ap-4339 46 20 schrödinger schrödinger ADJ ap-4339 46 21 equation equation NOUN ap-4339 46 22 from from ADP ap-4339 46 23 the the DET ap-4339 46 24 roots root NOUN ap-4339 46 25 of of ADP ap-4339 46 26 the the DET ap-4339 46 27 hankel hankel NOUN ap-4339 46 28 determinant determinant ADJ ap-4339 46 29 hd hd NOUN ap-4339 46 30 d(e d(e PROPN ap-4339 46 31 ) ) PUNCT ap-4339 46 32 = = SYM ap-4339 47 1 ∣∣∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣∣∣ PROPN ap-4339 47 2 fd+1 fd+1 NUM ap-4339 47 3 fd+2 fd+2 PROPN ap-4339 47 4 · · PUNCT ap-4339 47 5 · · PUNCT ap-4339 47 6 · · PUNCT ap-4339 48 1 fd+d fd+d PROPN ap-4339 48 2 fd+2 fd+2 PROPN ap-4339 48 3 fd+3 fd+3 X ap-4339 48 4 · · PUNCT ap-4339 48 5 · · PUNCT ap-4339 48 6 · · PUNCT ap-4339 48 7 fd+d+1 fd+d+1 NOUN ap-4339 48 8 ... ... PUNCT ap-4339 48 9 ... ... PUNCT ap-4339 48 10 . . PUNCT ap-4339 48 11 . . PUNCT ap-4339 48 12 . . PUNCT ap-4339 49 1 ... ... PUNCT ap-4339 50 1 fd+d fd+d PROPN ap-4339 50 2 fd+d+1 fd+d+1 X ap-4339 50 3 · · PUNCT ap-4339 50 4 · · PUNCT ap-4339 50 5 · · PUNCT ap-4339 51 1 fd+d−1 fd+d−1 PROPN ap-4339 51 2 ∣∣∣∣∣∣∣∣∣ ∣∣∣∣∣∣∣∣∣ PROPN ap-4339 51 3 = = SYM ap-4339 51 4 0 0 NUM ap-4339 51 5 , , PUNCT ap-4339 51 6 ( ( PUNCT ap-4339 51 7 5 5 NUM ap-4339 51 8 ) ) PUNCT ap-4339 51 9 where where SCONJ ap-4339 51 10 d d NOUN ap-4339 51 11 = = SYM ap-4339 51 12 2 2 NUM ap-4339 51 13 , , PUNCT ap-4339 51 14 3 3 NUM ap-4339 51 15 , , PUNCT ap-4339 51 16 . . PUNCT ap-4339 51 17 . . PUNCT ap-4339 51 18 . . PUNCT ap-4339 52 1 is be AUX ap-4339 52 2 the the DET ap-4339 52 3 dimension dimension NOUN ap-4339 52 4 of of ADP ap-4339 52 5 the the DET ap-4339 52 6 determinant determinant NOUN ap-4339 52 7 and and CCONJ ap-4339 52 8 d d NOUN ap-4339 52 9 is be AUX ap-4339 52 10 the the DET ap-4339 52 11 difference difference NOUN ap-4339 52 12 between between ADP ap-4339 52 13 the the DET ap-4339 52 14 degrees degree NOUN ap-4339 52 15 of of ADP ap-4339 52 16 the the DET ap-4339 52 17 polynomials polynomial NOUN ap-4339 52 18 in in ADP ap-4339 52 19 the the DET ap-4339 52 20 numerator numerator NOUN ap-4339 52 21 and and CCONJ ap-4339 52 22 denominator denominator NOUN ap-4339 52 23 of of ADP ap-4339 52 24 the the DET ap-4339 52 25 rational rational ADJ ap-4339 52 26 approximation approximation NOUN ap-4339 52 27 to to ADP ap-4339 52 28 f(x)[3–6 f(x)[3–6 PROPN ap-4339 52 29 ] ] PUNCT ap-4339 52 30 . . PUNCT ap-4339 53 1 in in ADP ap-4339 53 2 those those DET ap-4339 53 3 earlier early ADJ ap-4339 53 4 papers paper NOUN ap-4339 53 5 we we PRON ap-4339 53 6 have have AUX ap-4339 53 7 shown show VERB ap-4339 53 8 that that SCONJ ap-4339 53 9 there there PRON ap-4339 53 10 are be VERB ap-4339 53 11 sequences sequence NOUN ap-4339 53 12 of of ADP ap-4339 53 13 roots root NOUN ap-4339 53 14 e[d e[d NOUN ap-4339 53 15 , , PUNCT ap-4339 53 16 d d X ap-4339 53 17 ] ] X ap-4339 53 18 , , PUNCT ap-4339 53 19 d d X ap-4339 53 20 = = SYM ap-4339 53 21 2 2 NUM ap-4339 53 22 , , PUNCT ap-4339 53 23 3 3 NUM ap-4339 53 24 , , PUNCT ap-4339 53 25 . . PUNCT ap-4339 53 26 . . PUNCT ap-4339 54 1 . . PUNCT ap-4339 55 1 of of ADP ap-4339 55 2 the the DET ap-4339 55 3 determinant determinant ADJ ap-4339 55 4 hd hd NOUN ap-4339 55 5 d(e d(e PROPN ap-4339 55 6 ) ) PUNCT ap-4339 55 7 that that PRON ap-4339 55 8 converge converge VERB ap-4339 55 9 towards towards ADP ap-4339 55 10 the the DET ap-4339 55 11 bound bind VERB ap-4339 55 12 states state NOUN ap-4339 55 13 and and CCONJ ap-4339 55 14 resonances resonance NOUN ap-4339 55 15 of of ADP ap-4339 55 16 the the DET ap-4339 55 17 quantum quantum ADJ ap-4339 55 18 - - ADJ ap-4339 55 19 mechanical mechanical ADJ ap-4339 55 20 problem problem NOUN ap-4339 55 21 . . PUNCT ap-4339 56 1 we we PRON ap-4339 56 2 have have VERB ap-4339 56 3 at at ADP ap-4339 56 4 our our PRON ap-4339 56 5 disposal disposal NOUN ap-4339 56 6 a a DET ap-4339 56 7 set set NOUN ap-4339 56 8 of of ADP ap-4339 56 9 sequences sequence NOUN ap-4339 56 10 for for ADP ap-4339 56 11 each each DET ap-4339 56 12 value value NOUN ap-4339 56 13 of of ADP ap-4339 56 14 d d PROPN ap-4339 57 1 but but CCONJ ap-4339 57 2 it it PRON ap-4339 57 3 is be AUX ap-4339 57 4 commonly commonly ADV ap-4339 57 5 sufficient sufficient ADJ ap-4339 57 6 to to PART ap-4339 57 7 choose choose VERB ap-4339 57 8 d d NOUN ap-4339 57 9 = = SYM ap-4339 57 10 0 0 NUM ap-4339 57 11 . . PUNCT ap-4339 58 1 for for ADP ap-4339 58 2 this this DET ap-4339 58 3 reason reason NOUN ap-4339 58 4 , , PUNCT ap-4339 58 5 in in ADP ap-4339 58 6 this this DET ap-4339 58 7 paper paper NOUN ap-4339 58 8 we we PRON ap-4339 58 9 restrict restrict VERB ap-4339 58 10 ourselves ourselves PRON ap-4339 58 11 to to ADP ap-4339 58 12 the the DET ap-4339 58 13 sequences sequence NOUN ap-4339 58 14 of of ADP ap-4339 58 15 roots root NOUN ap-4339 58 16 e[d e[d NOUN ap-4339 58 17 ] ] X ap-4339 58 18 = = PUNCT ap-4339 58 19 e[d,0 e[d,0 PROPN ap-4339 58 20 ] ] PUNCT ap-4339 58 21 ( ( PUNCT ap-4339 58 22 unless unless SCONJ ap-4339 58 23 stated state VERB ap-4339 58 24 otherwise otherwise ADV ap-4339 58 25 ) ) PUNCT ap-4339 58 26 . . PUNCT ap-4339 59 1 in in ADP ap-4339 59 2 this this DET ap-4339 59 3 paper paper NOUN ap-4339 59 4 we we PRON ap-4339 59 5 are be AUX ap-4339 59 6 concerned concerned ADJ ap-4339 59 7 with with ADP ap-4339 59 8 anharmonic anharmonic ADJ ap-4339 59 9 - - PUNCT ap-4339 59 10 oscillator oscillator NOUN ap-4339 59 11 potentials potential NOUN ap-4339 59 12 of of ADP ap-4339 59 13 the the DET ap-4339 59 14 form form NOUN ap-4339 59 15 v v NOUN ap-4339 59 16 ( ( PUNCT ap-4339 59 17 x x NOUN ap-4339 59 18 ) ) PUNCT ap-4339 59 19 = = SYM ap-4339 60 1 k∑ k∑ PROPN ap-4339 60 2 j=1 j=1 PROPN ap-4339 60 3 vjx vjx VERB ap-4339 60 4 2j 2j NUM ap-4339 60 5 . . PUNCT ap-4339 61 1 ( ( PUNCT ap-4339 61 2 6 6 X ap-4339 61 3 ) ) PUNCT ap-4339 61 4 the the DET ap-4339 61 5 spectrum spectrum NOUN ap-4339 61 6 is be AUX ap-4339 61 7 discrete discrete ADJ ap-4339 61 8 when when SCONJ ap-4339 61 9 vk vk VERB ap-4339 61 10 > > X ap-4339 61 11 0 0 PUNCT ap-4339 62 1 and and CCONJ ap-4339 62 2 continuous continuous ADJ ap-4339 62 3 when when SCONJ ap-4339 62 4 vk vk ADP ap-4339 62 5 < < X ap-4339 62 6 0 0 NUM ap-4339 62 7 . . PUNCT ap-4339 63 1 in in ADP ap-4339 63 2 the the DET ap-4339 63 3 latter latter ADJ ap-4339 63 4 case case NOUN ap-4339 63 5 there there PRON ap-4339 63 6 may may AUX ap-4339 63 7 be be AUX ap-4339 63 8 resonances resonance NOUN ap-4339 63 9 embedded embed VERB ap-4339 63 10 in in ADP ap-4339 63 11 the the DET ap-4339 63 12 continuous continuous ADJ ap-4339 63 13 spectrum spectrum NOUN ap-4339 63 14 which which PRON ap-4339 63 15 are be AUX ap-4339 63 16 complex complex ADJ ap-4339 63 17 eigenvalues eigenvalue NOUN ap-4339 63 18 . . PUNCT ap-4339 64 1 the the DET ap-4339 64 2 real real ADJ ap-4339 64 3 part part NOUN ap-4339 64 4 of of ADP ap-4339 64 5 any any DET ap-4339 64 6 such such ADJ ap-4339 64 7 eigenvalue eigenvalue NOUN ap-4339 64 8 is be AUX ap-4339 64 9 the the DET ap-4339 64 10 resonance resonance NOUN ap-4339 64 11 position position NOUN ap-4339 64 12 and and CCONJ ap-4339 64 13 the the DET ap-4339 64 14 imaginary imaginary ADJ ap-4339 64 15 part part NOUN ap-4339 64 16 is be AUX ap-4339 64 17 half half DET ap-4339 64 18 its its PRON ap-4339 64 19 width width ADJ ap-4339 64 20 γ γ X ap-4339 64 21 ( ( PUNCT ap-4339 64 22 |=e| |=e| NUM ap-4339 64 23 = = SYM ap-4339 64 24 γ/2 γ/2 NUM ap-4339 64 25 ) ) PUNCT ap-4339 64 26 . . PUNCT ap-4339 65 1 3 3 X ap-4339 65 2 . . X ap-4339 65 3 examples example NOUN ap-4339 65 4 four four NUM ap-4339 65 5 examples example NOUN ap-4339 65 6 chosen choose VERB ap-4339 65 7 by by ADP ap-4339 65 8 gaudreau gaudreau PROPN ap-4339 65 9 et et NOUN ap-4339 65 10 al[1 al[1 PROPN ap-4339 65 11 ] ] PUNCT ap-4339 65 12 are be AUX ap-4339 65 13 quasi quasi ADJ ap-4339 65 14 - - ADJ ap-4339 65 15 exactly exactly ADV ap-4339 65 16 solvable solvable ADJ ap-4339 65 17 problems problem NOUN ap-4339 65 18 ; ; PUNCT ap-4339 65 19 that that PRON ap-4339 65 20 is be AUX ap-4339 65 21 to to PART ap-4339 65 22 say say VERB ap-4339 65 23 , , PUNCT ap-4339 65 24 one one PRON ap-4339 65 25 can can AUX ap-4339 65 26 obtain obtain VERB ap-4339 65 27 exact exact ADJ ap-4339 65 28 solutions solution NOUN ap-4339 65 29 for for ADP ap-4339 65 30 some some DET ap-4339 65 31 states state NOUN ap-4339 65 32 : : PUNCT ap-4339 65 33 v1(x v1(x NUM ap-4339 65 34 ) ) PUNCT ap-4339 65 35 = = SYM ap-4339 66 1 x2 x2 ADP ap-4339 66 2 − − PROPN ap-4339 67 1 4x4 4x4 NUM ap-4339 68 1 + + NUM ap-4339 68 2 x6 x6 PROPN ap-4339 68 3 e0 e0 NOUN ap-4339 68 4 = = PUNCT ap-4339 68 5 −2 −2 PROPN ap-4339 68 6 v2(x v2(x NOUN ap-4339 68 7 ) ) PUNCT ap-4339 68 8 = = SYM ap-4339 68 9 4x2 4x2 NUM ap-4339 68 10 − − NUM ap-4339 68 11 6x4 6x4 NUM ap-4339 68 12 + + CCONJ ap-4339 68 13 x6 x6 PROPN ap-4339 68 14 e1 e1 NOUN ap-4339 68 15 = = PUNCT ap-4339 68 16 −9 −9 NOUN ap-4339 68 17 v3(x v3(x NOUN ap-4339 68 18 ) ) PUNCT ap-4339 68 19 = = SYM ap-4339 68 20 105 105 NUM ap-4339 68 21 64 64 NUM ap-4339 68 22 x x SYM ap-4339 68 23 2 2 NUM ap-4339 68 24 − − NUM ap-4339 68 25 43 43 NUM ap-4339 68 26 8 8 NUM ap-4339 68 27 x x SYM ap-4339 68 28 4 4 NUM ap-4339 68 29 + + NUM ap-4339 68 30 x6 x6 PROPN ap-4339 68 31 − − PROPN ap-4339 68 32 x8 x8 PROPN ap-4339 68 33 + + CCONJ ap-4339 68 34 x10 x10 NUM ap-4339 68 35 e0 e0 NOUN ap-4339 68 36 = = PUNCT ap-4339 68 37 3 3 NUM ap-4339 68 38 8 8 NUM ap-4339 68 39 v4(x v4(x NOUN ap-4339 68 40 ) ) PUNCT ap-4339 68 41 = = SYM ap-4339 68 42 169 169 NUM ap-4339 68 43 64 64 NUM ap-4339 68 44 x x SYM ap-4339 68 45 2 2 NUM ap-4339 68 46 − − NUM ap-4339 68 47 59 59 NUM ap-4339 68 48 8 8 NUM ap-4339 68 49 x x SYM ap-4339 68 50 4 4 NUM ap-4339 68 51 + + NUM ap-4339 68 52 x6 x6 PROPN ap-4339 68 53 − − PROPN ap-4339 68 54 x8 x8 PROPN ap-4339 68 55 + + CCONJ ap-4339 68 56 x10 x10 NUM ap-4339 68 57 e1 e1 NOUN ap-4339 68 58 = = NOUN ap-4339 68 59 9 9 NUM ap-4339 68 60 8 8 NUM ap-4339 68 61 . . PUNCT ap-4339 69 1 ( ( PUNCT ap-4339 69 2 7 7 NUM ap-4339 69 3 ) ) PUNCT ap-4339 69 4 392 392 NUM ap-4339 69 5 vol vol NOUN ap-4339 69 6 . . PUNCT ap-4339 70 1 57 57 NUM ap-4339 70 2 no no NOUN ap-4339 70 3 . . PUNCT ap-4339 71 1 6/2017 6/2017 NUM ap-4339 71 2 one one NUM ap-4339 71 3 - - PUNCT ap-4339 71 4 dimensional dimensional ADJ ap-4339 71 5 anharmonic anharmonic ADJ ap-4339 71 6 oscillators oscillator NOUN ap-4339 71 7 the the DET ap-4339 71 8 rpm rpm NOUN ap-4339 71 9 yields yield NOUN ap-4339 71 10 the the DET ap-4339 71 11 exact exact ADJ ap-4339 71 12 result result NOUN ap-4339 71 13 for for ADP ap-4339 71 14 all all DET ap-4339 71 15 these these DET ap-4339 71 16 particular particular ADJ ap-4339 71 17 cases case NOUN ap-4339 71 18 because because SCONJ ap-4339 71 19 in in ADP ap-4339 71 20 all all PRON ap-4339 71 21 of of ADP ap-4339 71 22 them they PRON ap-4339 71 23 the the DET ap-4339 71 24 logarithmic logarithmic ADJ ap-4339 71 25 derivative derivative ADJ ap-4339 71 26 f f X ap-4339 71 27 ( ( PUNCT ap-4339 71 28 x x X ap-4339 71 29 ) ) PUNCT ap-4339 71 30 is be AUX ap-4339 71 31 a a DET ap-4339 71 32 rational rational ADJ ap-4339 71 33 function function NOUN ap-4339 71 34 of of ADP ap-4339 71 35 the the DET ap-4339 71 36 coordinate coordinate NOUN ap-4339 71 37 . . PUNCT ap-4339 72 1 the the DET ap-4339 72 2 hankel hankel NOUN ap-4339 72 3 determinants determinant NOUN ap-4339 72 4 of of ADP ap-4339 72 5 lowest low ADJ ap-4339 72 6 dimension dimension NOUN ap-4339 72 7 for for ADP ap-4339 72 8 each each DET ap-4339 72 9 case case NOUN ap-4339 72 10 are be AUX ap-4339 72 11 : : PUNCT ap-4339 72 12 h0 h0 NOUN ap-4339 72 13 2 2 NUM ap-4339 72 14 ( ( PUNCT ap-4339 72 15 e e NOUN ap-4339 72 16 ) ) PUNCT ap-4339 72 17 = = SYM ap-4339 72 18 1 1 NUM ap-4339 72 19 4725(e 4725(e NOUN ap-4339 72 20 + + CCONJ ap-4339 72 21 2)(e5 2)(e5 NUM ap-4339 72 22 − − NOUN ap-4339 72 23 2e4 2e4 NUM ap-4339 72 24 − − NOUN ap-4339 72 25 23e3 23e3 NUM ap-4339 72 26 − − NUM ap-4339 72 27 602e2 602e2 NUM ap-4339 72 28 + + NUM ap-4339 72 29 1030e 1030e NUM ap-4339 72 30 − − PROPN ap-4339 72 31 1412 1412 NUM ap-4339 72 32 ) ) PUNCT ap-4339 72 33 , , PUNCT ap-4339 72 34 ( ( PUNCT ap-4339 72 35 8) 8) NUM ap-4339 72 36 h0 h0 NOUN ap-4339 72 37 2 2 NUM ap-4339 72 38 ( ( PUNCT ap-4339 72 39 e e NOUN ap-4339 72 40 ) ) PUNCT ap-4339 72 41 = = SYM ap-4339 72 42 1 1 NUM ap-4339 72 43 4465125(e 4465125(e NOUN ap-4339 73 1 + + NOUN ap-4339 73 2 9)(e5 9)(e5 NUM ap-4339 73 3 − − NUM ap-4339 73 4 9e4 9e4 NUM ap-4339 73 5 − − PROPN ap-4339 73 6 187e3 187e3 NUM ap-4339 74 1 − − PROPN ap-4339 74 2 8217e2 8217e2 PROPN ap-4339 74 3 + + CCONJ ap-4339 74 4 78336e 78336e NUM ap-4339 74 5 − − PROPN ap-4339 74 6 348624 348624 NUM ap-4339 74 7 ) ) PUNCT ap-4339 74 8 , , PUNCT ap-4339 74 9 ( ( PUNCT ap-4339 74 10 9 9 X ap-4339 74 11 ) ) PUNCT ap-4339 74 12 h0 h0 NOUN ap-4339 74 13 3 3 NUM ap-4339 74 14 ( ( PUNCT ap-4339 74 15 e e NOUN ap-4339 74 16 ) ) PUNCT ap-4339 74 17 = = SYM ap-4339 74 18 1 1 NUM ap-4339 74 19 3189612751764848640000(8e 3189612751764848640000(8e NUM ap-4339 74 20 − − PROPN ap-4339 74 21 3)(8589934592e11 3)(8589934592e11 NUM ap-4339 74 22 + + NUM ap-4339 74 23 3221225472e10 3221225472e10 NUM ap-4339 74 24 − − NOUN ap-4339 74 25 1887235473408e9 1887235473408e9 PROPN ap-4339 74 26 − − PROPN ap-4339 75 1 399347250364416e8 399347250364416e8 NUM ap-4339 75 2 − − PROPN ap-4339 75 3 1634745666502656e7 1634745666502656e7 PROPN ap-4339 76 1 + + CCONJ ap-4339 77 1 10770225531715584e6 10770225531715584e6 NUM ap-4339 78 1 − − NOUN ap-4339 78 2 836065166572191744e5 836065166572191744e5 NOUN ap-4339 78 3 − − NOUN ap-4339 78 4 905684630058491904e4 905684630058491904e4 NOUN ap-4339 79 1 + + CCONJ ap-4339 80 1 5197219286067104256e3 5197219286067104256e3 NUM ap-4339 80 2 − − NOUN ap-4339 80 3 2944302537136698432e2 2944302537136698432e2 PROPN ap-4339 80 4 − − PROPN ap-4339 80 5 12283878786837315912e 12283878786837315912e NUM ap-4339 80 6 + + CCONJ ap-4339 80 7 22452709866105906693 22452709866105906693 NUM ap-4339 80 8 ) ) PUNCT ap-4339 80 9 , , PUNCT ap-4339 80 10 ( ( PUNCT ap-4339 80 11 10 10 X ap-4339 80 12 ) ) PUNCT ap-4339 80 13 h0 h0 NOUN ap-4339 80 14 3 3 NUM ap-4339 80 15 ( ( PUNCT ap-4339 80 16 e e NOUN ap-4339 80 17 ) ) PUNCT ap-4339 80 18 = = SYM ap-4339 80 19 1 1 NUM ap-4339 80 20 431028319209742820966400000(8e 431028319209742820966400000(8e NUM ap-4339 81 1 − − NUM ap-4339 81 2 9)(8589934592e11 9)(8589934592e11 NUM ap-4339 81 3 + + NUM ap-4339 81 4 9663676416e10 9663676416e10 NUM ap-4339 81 5 − − NOUN ap-4339 82 1 5569096187904e9 5569096187904e9 NUM ap-4339 83 1 − − PROPN ap-4339 83 2 2064531673055232e8 2064531673055232e8 NUM ap-4339 84 1 − − NOUN ap-4339 84 2 15362232560910336e7 15362232560910336e7 PROPN ap-4339 85 1 + + X ap-4339 85 2 158709729905344512e6 158709729905344512e6 NUM ap-4339 86 1 − − NOUN ap-4339 86 2 23752960275863896064e5 23752960275863896064e5 NUM ap-4339 87 1 − − NOUN ap-4339 87 2 84068173973645402112e4 84068173973645402112e4 PROPN ap-4339 88 1 + + NUM ap-4339 88 2 2318080070178601634304e3 2318080070178601634304e3 NUM ap-4339 89 1 − − NOUN ap-4339 89 2 6274577633554290840768e2 6274577633554290840768e2 NOUN ap-4339 89 3 − − NOUN ap-4339 89 4 75410626140297229262472e 75410626140297229262472e NUM ap-4339 89 5 + + CCONJ ap-4339 89 6 655367638076442656931879 655367638076442656931879 NUM ap-4339 89 7 ) ) PUNCT ap-4339 89 8 , , PUNCT ap-4339 89 9 ( ( PUNCT ap-4339 89 10 11 11 NUM ap-4339 89 11 ) ) PUNCT ap-4339 89 12 respectively respectively ADV ap-4339 89 13 . . PUNCT ap-4339 90 1 it it PRON ap-4339 90 2 is be AUX ap-4339 90 3 clear clear ADJ ap-4339 90 4 that that SCONJ ap-4339 90 5 the the DET ap-4339 90 6 second second ADJ ap-4339 90 7 factor factor NOUN ap-4339 90 8 of of ADP ap-4339 90 9 each each DET ap-4339 90 10 hankel hankel NOUN ap-4339 90 11 determinant determinant ADJ ap-4339 90 12 yields yield VERB ap-4339 90 13 the the DET ap-4339 90 14 exact exact ADJ ap-4339 90 15 eigenvalue eigenvalue NOUN ap-4339 90 16 of of ADP ap-4339 90 17 the the DET ap-4339 90 18 corresponding corresponding ADJ ap-4339 90 19 model model NOUN ap-4339 90 20 in in ADP ap-4339 90 21 equation equation NOUN ap-4339 90 22 ( ( PUNCT ap-4339 90 23 7 7 NUM ap-4339 90 24 ) ) PUNCT ap-4339 90 25 . . PUNCT ap-4339 91 1 as as ADP ap-4339 91 2 a a DET ap-4339 91 3 nontrivial nontrivial ADJ ap-4339 91 4 example example NOUN ap-4339 91 5 we we PRON ap-4339 91 6 consider consider VERB ap-4339 91 7 the the DET ap-4339 91 8 quartic quartic ADJ ap-4339 91 9 anharmonic anharmonic ADJ ap-4339 91 10 oscillator oscillator NOUN ap-4339 91 11 v v NOUN ap-4339 91 12 ( ( PUNCT ap-4339 91 13 x x NOUN ap-4339 91 14 ) ) PUNCT ap-4339 91 15 = = SYM ap-4339 92 1 x2 x2 PROPN ap-4339 93 1 + + CCONJ ap-4339 93 2 λx4 λx4 ADJ ap-4339 93 3 . . PUNCT ap-4339 94 1 ( ( PUNCT ap-4339 94 2 12 12 NUM ap-4339 94 3 ) ) PUNCT ap-4339 94 4 gaudreau gaudreau PROPN ap-4339 94 5 et et PROPN ap-4339 94 6 al al PROPN ap-4339 95 1 [ [ X ap-4339 95 2 1 1 X ap-4339 95 3 ] ] PUNCT ap-4339 95 4 calculated calculate VERB ap-4339 95 5 the the DET ap-4339 95 6 ground ground NOUN ap-4339 95 7 state state NOUN ap-4339 95 8 for for ADP ap-4339 95 9 λ λ X ap-4339 95 10 = = NOUN ap-4339 95 11 1 1 NUM ap-4339 95 12 with with ADP ap-4339 95 13 remarkable remarkable ADJ ap-4339 95 14 accuracy accuracy NOUN ap-4339 95 15 . . PUNCT ap-4339 96 1 the the DET ap-4339 96 2 rpm rpm NOUN ap-4339 96 3 also also ADV ap-4339 96 4 enables enable VERB ap-4339 96 5 great great ADJ ap-4339 96 6 accuracy accuracy NOUN ap-4339 96 7 because because SCONJ ap-4339 96 8 of of ADP ap-4339 96 9 its its PRON ap-4339 96 10 exponential exponential ADJ ap-4339 96 11 convergence convergence NOUN ap-4339 96 12 . . PUNCT ap-4339 97 1 for for ADP ap-4339 97 2 example example NOUN ap-4339 97 3 , , PUNCT ap-4339 97 4 with with ADP ap-4339 97 5 determinants determinant NOUN ap-4339 97 6 of of ADP ap-4339 97 7 dimension dimension NOUN ap-4339 97 8 d d PROPN ap-4339 97 9 ≤ ≤ NUM ap-4339 97 10 623 623 NUM ap-4339 97 11 we we PRON ap-4339 97 12 obtained obtain VERB ap-4339 97 13 e0 e0 PROPN ap-4339 97 14 = = PROPN ap-4339 97 15 1.39235164153029185565750787660993418460006671122083408890634932387756743187564652 1.39235164153029185565750787660993418460006671122083408890634932387756743187564652 NUM ap-4339 97 16 85909735634677917591211513753417388174455516240463837130438178697370013460935168 85909735634677917591211513753417388174455516240463837130438178697370013460935168 NUM ap-4339 97 17 15484208574889656901800305541236648743218953435715417409382624057229519998568711 15484208574889656901800305541236648743218953435715417409382624057229519998568711 NUM ap-4339 97 18 18140968922702273638169811112603107034293861341959645684859182914634898518858148 18140968922702273638169811112603107034293861341959645684859182914634898518858148 NUM ap-4339 97 19 63025469392145221031177208948219643654580541741801366088701870825264349698158700 63025469392145221031177208948219643654580541741801366088701870825264349698158700 NUM ap-4339 97 20 82340760759574319226851138960019685449394982096240756162094619633463447377455701 82340760759574319226851138960019685449394982096240756162094619633463447377455701 NUM ap-4339 97 21 49211492623468905916373385630626814055709925106270580909505786666030935831448351 49211492623468905916373385630626814055709925106270580909505786666030935831448351 NUM ap-4339 97 22 97352905560061049224302849821825415119194035000689109989896675454979833183805654 97352905560061049224302849821825415119194035000689109989896675454979833183805654 NUM ap-4339 97 23 19975466162573031052729404581567529262538228672118076018319975294595611113245756 19975466162573031052729404581567529262538228672118076018319975294595611113245756 NUM ap-4339 97 24 78445653018419567798509749315372254188588216960225999726980950846580656370213654 78445653018419567798509749315372254188588216960225999726980950846580656370213654 NUM ap-4339 97 25 47651793869049904755455309191949465274340562585980971938979595684138772300267900 47651793869049904755455309191949465274340562585980971938979595684138772300267900 NUM ap-4339 97 26 68177673277845708654477245631366268184519934644126051969150124972306172724393638 68177673277845708654477245631366268184519934644126051969150124972306172724393638 NUM ap-4339 97 27 74511499751517142498813649966422950045954851519165072488133686158144218817306000 74511499751517142498813649966422950045954851519165072488133686158144218817306000 NUM ap-4339 97 28 39773536840117104637678735672726392478420532548924901523470626991951440934018875 39773536840117104637678735672726392478420532548924901523470626991951440934018875 NUM ap-4339 97 29 83071929546817823113125377471312004221881276679422460872268510606766179549130792 83071929546817823113125377471312004221881276679422460872268510606766179549130792 NUM ap-4339 97 30 640798558850522732484547554994100518213983 640798558850522732484547554994100518213983 NUM ap-4339 97 31 , , PUNCT ap-4339 97 32 which which PRON ap-4339 97 33 is be AUX ap-4339 97 34 considerably considerably ADV ap-4339 97 35 more more ADV ap-4339 97 36 accurate accurate ADJ ap-4339 97 37 than than ADP ap-4339 97 38 the the DET ap-4339 97 39 result result NOUN ap-4339 97 40 reported report VERB ap-4339 97 41 by by ADP ap-4339 97 42 those those DET ap-4339 97 43 authors author NOUN ap-4339 97 44 . . PUNCT ap-4339 98 1 such such DET ap-4339 98 2 an an DET ap-4339 98 3 accuracy accuracy NOUN ap-4339 98 4 is be AUX ap-4339 98 5 unnecessary unnecessary ADJ ap-4339 98 6 but but CCONJ ap-4339 98 7 it it PRON ap-4339 98 8 clearly clearly ADV ap-4339 98 9 shows show VERB ap-4339 98 10 the the DET ap-4339 98 11 stability stability NOUN ap-4339 98 12 and and CCONJ ap-4339 98 13 remarkable remarkable ADJ ap-4339 98 14 rate rate NOUN ap-4339 98 15 of of ADP ap-4339 98 16 convergence convergence NOUN ap-4339 98 17 of of ADP ap-4339 98 18 the the DET ap-4339 98 19 rpm rpm NOUN ap-4339 98 20 . . PUNCT ap-4339 99 1 for for ADP ap-4339 99 2 some some DET ap-4339 99 3 approaches approach NOUN ap-4339 99 4 the the DET ap-4339 99 5 pure pure ADJ ap-4339 99 6 quartic quartic ADJ ap-4339 99 7 oscillator oscillator NOUN ap-4339 99 8 v v NOUN ap-4339 99 9 ( ( PUNCT ap-4339 99 10 x x NOUN ap-4339 99 11 ) ) PUNCT ap-4339 99 12 = = SYM ap-4339 99 13 x4 x4 PROPN ap-4339 99 14 ( ( PUNCT ap-4339 99 15 13 13 NUM ap-4339 99 16 ) ) PUNCT ap-4339 99 17 393 393 NUM ap-4339 99 18 francisco francisco PROPN ap-4339 99 19 marcelo marcelo PROPN ap-4339 99 20 fernández fernández PROPN ap-4339 99 21 , , PUNCT ap-4339 99 22 javier javier PROPN ap-4339 99 23 garcia garcia PROPN ap-4339 99 24 acta acta PROPN ap-4339 99 25 polytechnica polytechnica PROPN ap-4339 99 26 may may AUX ap-4339 99 27 be be AUX ap-4339 99 28 more more ADV ap-4339 99 29 demanding demanding ADJ ap-4339 99 30 than than SCONJ ap-4339 99 31 the the DET ap-4339 99 32 oscillator oscillator NOUN ap-4339 99 33 treated treat VERB ap-4339 99 34 previously previously ADV ap-4339 99 35 . . PUNCT ap-4339 100 1 however however ADV ap-4339 100 2 , , PUNCT ap-4339 100 3 this this PRON ap-4339 100 4 is be AUX ap-4339 100 5 not not PART ap-4339 100 6 the the DET ap-4339 100 7 case case NOUN ap-4339 100 8 for for ADP ap-4339 100 9 the the DET ap-4339 100 10 rpm rpm NOUN ap-4339 100 11 that that PRON ap-4339 100 12 yields yield VERB ap-4339 100 13 e0 e0 PROPN ap-4339 100 14 = = PUNCT ap-4339 101 1 1.06036209048418289964704601669266354551520872852829779332162452416959435630443444 1.06036209048418289964704601669266354551520872852829779332162452416959435630443444 NUM ap-4339 101 2 21126896299134671720351054624435858252558087980821029314701317683637238249357892 21126896299134671720351054624435858252558087980821029314701317683637238249357892 NUM ap-4339 101 3 26246004708175446960141637488417282256290593575779088806178879026360154939569027 26246004708175446960141637488417282256290593575779088806178879026360154939569027 NUM ap-4339 101 4 51961489200942934873584409442694897901213971464290951923352453382834703350575761 51961489200942934873584409442694897901213971464290951923352453382834703350575761 NUM ap-4339 101 5 51120257039888523720240221842110308657373109139891545365841031116794058335486020 51120257039888523720240221842110308657373109139891545365841031116794058335486020 NUM ap-4339 101 6 09227440069631126702388622971429699610592155832226671376935508673610000831830027 09227440069631126702388622971429699610592155832226671376935508673610000831830027 NUM ap-4339 101 7 51792623357391390621361807764985969618149941279280927284070795610604240722946809 51792623357391390621361807764985969618149941279280927284070795610604240722946809 NUM ap-4339 101 8 94913627572927387279136890279842472226217169444889547513704380684054391877877295 94913627572927387279136890279842472226217169444889547513704380684054391877877295 NUM ap-4339 101 9 32342458274372543178323190603810687416044034374530146847272813918612940470431034 32342458274372543178323190603810687416044034374530146847272813918612940470431034 NUM ap-4339 101 10 01351071607110353008929823272542766151898695056504716025275608952626219102568822 01351071607110353008929823272542766151898695056504716025275608952626219102568822 NUM ap-4339 101 11 00964410287815640052705292932405076382650282591122477362538471854714402572285438 00964410287815640052705292932405076382650282591122477362538471854714402572285438 NUM ap-4339 101 12 48529745045857097828402490669995704768445877091762029124375273254907211643344023 48529745045857097828402490669995704768445877091762029124375273254907211643344023 NUM ap-4339 101 13 02947306923981908956853745359884460160202313291933059395869304916644281633946163 02947306923981908956853745359884460160202313291933059395869304916644281633946163 NUM ap-4339 101 14 32428700242614612377430099522342042085977356901535654168502308941851348795734106 32428700242614612377430099522342042085977356901535654168502308941851348795734106 NUM ap-4339 101 15 58547971946759646679661346762885864379526545195605682867159583388847434670120422 58547971946759646679661346762885864379526545195605682867159583388847434670120422 NUM ap-4339 101 16 42071491874787103842957338913898524589402226347126961769965604409311709985471606 42071491874787103842957338913898524589402226347126961769965604409311709985471606 NUM ap-4339 101 17 46641857421281143028818111495112214843140887121662059313076923418022298272468836 46641857421281143028818111495112214843140887121662059313076923418022298272468836 NUM ap-4339 101 18 26045356507913236221596486925870033200274440968806404623978817839469837807048268 26045356507913236221596486925870033200274440968806404623978817839469837807048268 NUM ap-4339 101 19 60217427219460350750696191658224983009606134572666392863592217643534013718920448 60217427219460350750696191658224983009606134572666392863592217643534013718920448 NUM ap-4339 101 20 14846483730289412529638634402446954353934473733433447707230478215508820964235121 14846483730289412529638634402446954353934473733433447707230478215508820964235121 NUM ap-4339 101 21 06900382833900237848230939194834 06900382833900237848230939194834 NUM ap-4339 101 22 from from ADP ap-4339 101 23 determinants determinant NOUN ap-4339 101 24 of of ADP ap-4339 101 25 dimension dimension NOUN ap-4339 101 26 d d PROPN ap-4339 101 27 ≤ ≤ NOUN ap-4339 101 28 806 806 NUM ap-4339 101 29 . . PUNCT ap-4339 102 1 we we PRON ap-4339 102 2 think think VERB ap-4339 102 3 that that SCONJ ap-4339 102 4 present present ADJ ap-4339 102 5 result result NOUN ap-4339 102 6 is be AUX ap-4339 102 7 more more ADV ap-4339 102 8 accurate accurate ADJ ap-4339 102 9 than than ADP ap-4339 102 10 the the DET ap-4339 102 11 one one NOUN ap-4339 102 12 reported report VERB ap-4339 102 13 by by ADP ap-4339 102 14 trott[2 trott[2 PROPN ap-4339 102 15 ] ] PUNCT ap-4339 102 16 , , PUNCT ap-4339 102 17 the the DET ap-4339 102 18 discrepancy discrepancy NOUN ap-4339 102 19 being be AUX ap-4339 102 20 in in ADP ap-4339 102 21 his his PRON ap-4339 102 22 last last ADJ ap-4339 102 23 9 9 NUM ap-4339 102 24 figures figure NOUN ap-4339 102 25 . . PUNCT ap-4339 103 1 in in ADP ap-4339 103 2 the the DET ap-4339 103 3 case case NOUN ap-4339 103 4 of of ADP ap-4339 103 5 the the DET ap-4339 103 6 quartic quartic ADJ ap-4339 103 7 anharmonic anharmonic ADJ ap-4339 103 8 oscillators oscillator NOUN ap-4339 103 9 ( ( PUNCT ap-4339 103 10 6 6 NUM ap-4339 103 11 ) ) PUNCT ap-4339 103 12 and and CCONJ ap-4339 103 13 ( ( PUNCT ap-4339 103 14 12 12 NUM ap-4339 103 15 ) ) PUNCT ap-4339 103 16 it it PRON ap-4339 103 17 was be AUX ap-4339 103 18 proved prove VERB ap-4339 103 19 that that SCONJ ap-4339 103 20 e[d,0 e[d,0 PROPN ap-4339 103 21 ] ] PUNCT ap-4339 103 22 0 0 PUNCT ap-4339 103 23 and and CCONJ ap-4339 103 24 e[d,1 e[d,1 PROPN ap-4339 103 25 ] ] X ap-4339 103 26 0 0 NUM ap-4339 103 27 are be AUX ap-4339 103 28 lower low ADJ ap-4339 103 29 and and CCONJ ap-4339 103 30 upper upper ADJ ap-4339 103 31 bounds bound NOUN ap-4339 103 32 to to ADP ap-4339 103 33 the the DET ap-4339 103 34 actual actual ADJ ap-4339 103 35 eigenvalue eigenvalue NOUN ap-4339 103 36 , , PUNCT ap-4339 103 37 respectively[3 respectively[3 PROPN ap-4339 103 38 , , PUNCT ap-4339 103 39 4 4 NUM ap-4339 103 40 ] ] PUNCT ap-4339 103 41 . . PUNCT ap-4339 104 1 in in ADP ap-4339 104 2 order order NOUN ap-4339 104 3 to to PART ap-4339 104 4 verify verify VERB ap-4339 104 5 the the DET ap-4339 104 6 accuracy accuracy NOUN ap-4339 104 7 of of ADP ap-4339 104 8 present present ADJ ap-4339 104 9 calculation calculation NOUN ap-4339 104 10 we we PRON ap-4339 104 11 verified verify VERB ap-4339 104 12 that that SCONJ ap-4339 104 13 both both DET ap-4339 104 14 bounds bound NOUN ap-4339 104 15 agreed agree VERB ap-4339 104 16 to to ADP ap-4339 104 17 the the DET ap-4339 104 18 last last ADJ ap-4339 104 19 digit digit NOUN ap-4339 104 20 . . PUNCT ap-4339 105 1 as as SCONJ ap-4339 105 2 stated state VERB ap-4339 105 3 in in ADP ap-4339 105 4 the the DET ap-4339 105 5 introduction introduction NOUN ap-4339 105 6 , , PUNCT ap-4339 105 7 the the DET ap-4339 105 8 rpm rpm NOUN ap-4339 105 9 yields yield NOUN ap-4339 105 10 not not PART ap-4339 105 11 only only ADV ap-4339 105 12 the the DET ap-4339 105 13 bound bind VERB ap-4339 105 14 states state NOUN ap-4339 105 15 but but CCONJ ap-4339 105 16 also also ADV ap-4339 105 17 the the DET ap-4339 105 18 resonances resonance NOUN ap-4339 105 19 . . PUNCT ap-4339 106 1 for for ADP ap-4339 106 2 example example NOUN ap-4339 106 3 , , PUNCT ap-4339 106 4 in in ADP ap-4339 106 5 the the DET ap-4339 106 6 case case NOUN ap-4339 106 7 of of ADP ap-4339 106 8 the the DET ap-4339 106 9 anharmonic anharmonic ADJ ap-4339 106 10 oscillator oscillator NOUN ap-4339 106 11 ( ( PUNCT ap-4339 106 12 12 12 NUM ap-4339 106 13 ) ) PUNCT ap-4339 106 14 with with ADP ap-4339 106 15 λ λ X ap-4339 106 16 = = PUNCT ap-4339 106 17 −0.1 −0.1 PROPN ap-4339 106 18 ( ( PUNCT ap-4339 106 19 inverted inverted ADJ ap-4339 106 20 double double ADJ ap-4339 106 21 well well ADV ap-4339 106 22 ) ) PUNCT ap-4339 106 23 we we PRON ap-4339 106 24 obtain obtain VERB ap-4339 106 25 < < X ap-4339 106 26 e e X ap-4339 106 27 = = NOUN ap-4339 106 28 0.90067290409201502480472168921028775830460331662203069831718516924034871463944702 0.90067290409201502480472168921028775830460331662203069831718516924034871463944702 NUM ap-4339 106 29 49616726790089628268825293776377464732577257777502973177491351445742473385877709 49616726790089628268825293776377464732577257777502973177491351445742473385877709 NUM ap-4339 106 30 26803971267801469755869917579845522512000205420137720995176766371327034480743071 26803971267801469755869917579845522512000205420137720995176766371327034480743071 NUM ap-4339 106 31 07713982008790873985646991861751535214021599017867320106022879739539457665858699 07713982008790873985646991861751535214021599017867320106022879739539457665858699 NUM ap-4339 106 32 75562973189279258249081617920321264175746331544068756411634377154244333590011287 75562973189279258249081617920321264175746331544068756411634377154244333590011287 NUM ap-4339 106 33 04230510965330925907792495147669628533284309302211234477027796391708328562113084 04230510965330925907792495147669628533284309302211234477027796391708328562113084 NUM ap-4339 106 34 41726909573060442238866068277795715277616928060425810097530790289082978267983213 41726909573060442238866068277795715277616928060425810097530790289082978267983213 NUM ap-4339 106 35 67842682657484596201757300110536533702699585361715680944542285361299988968687820 67842682657484596201757300110536533702699585361715680944542285361299988968687820 NUM ap-4339 106 36 12308852365127364727689632938045419946222831027030494463529154344400824268783119 12308852365127364727689632938045419946222831027030494463529154344400824268783119 NUM ap-4339 106 37 49185729315006099566578108828241145777722487108371656443716078796497379465206234 49185729315006099566578108828241145777722487108371656443716078796497379465206234 NUM ap-4339 106 38 879130342123770426063990565158077971857506099342729619 879130342123770426063990565158077971857506099342729619 NUM ap-4339 106 39 and and CCONJ ap-4339 106 40 |=e| |=e| NUM ap-4339 106 41 = = SYM ap-4339 107 1 0.00669328087580013026927187508131824112294989432621696735893314097282610915605850 0.00669328087580013026927187508131824112294989432621696735893314097282610915605850 NUM ap-4339 107 2 43018393541639674627243621481357409744100069700186351017147154410094249647120952 43018393541639674627243621481357409744100069700186351017147154410094249647120952 NUM ap-4339 107 3 59566361194259386325794519366933621549298669570727785778446401403144312336955986 59566361194259386325794519366933621549298669570727785778446401403144312336955986 NUM ap-4339 107 4 73980375283541840546888210884788662488801718718713379746362368368461205368517345 73980375283541840546888210884788662488801718718713379746362368368461205368517345 NUM ap-4339 107 5 68189777241623332803606777032301489912446298837896455581815166460445660555875128 68189777241623332803606777032301489912446298837896455581815166460445660555875128 NUM ap-4339 107 6 54363903733935667870354171283504808639418360504429532217074896601384341982511525 54363903733935667870354171283504808639418360504429532217074896601384341982511525 NUM ap-4339 107 7 91876064523830978322014707732840778218698514295641443748495983816659272161010695 91876064523830978322014707732840778218698514295641443748495983816659272161010695 NUM ap-4339 107 8 96118632431428217783653913815974284318203202992357388742962705328614872135008968 96118632431428217783653913815974284318203202992357388742962705328614872135008968 NUM ap-4339 107 9 45311943228106834110088574337059948926573991903248493789402558550272582426356810 45311943228106834110088574337059948926573991903248493789402558550272582426356810 NUM ap-4339 107 10 29615386184966870885537480832794653421556685850226225141032328397825281636792728 29615386184966870885537480832794653421556685850226225141032328397825281636792728 NUM ap-4339 107 11 913688704017585002638602666568373554869393536520227140 913688704017585002638602666568373554869393536520227140 NUM ap-4339 107 12 394 394 NUM ap-4339 107 13 vol vol NOUN ap-4339 107 14 . . PUNCT ap-4339 108 1 57 57 NUM ap-4339 108 2 no no NOUN ap-4339 108 3 . . PUNCT ap-4339 109 1 6/2017 6/2017 NUM ap-4339 109 2 one one NUM ap-4339 109 3 - - PUNCT ap-4339 109 4 dimensional dimensional ADJ ap-4339 109 5 anharmonic anharmonic ADJ ap-4339 109 6 oscillators oscillator NOUN ap-4339 109 7 0.0 0.0 NUM ap-4339 109 8 0.2 0.2 NUM ap-4339 109 9 0.4 0.4 NUM ap-4339 109 10 0.6 0.6 NUM ap-4339 109 11 0.8 0.8 NUM ap-4339 109 12 1.0 1.0 NUM ap-4339 109 13 0.0 0.0 NUM ap-4339 109 14 0.4 0.4 NUM ap-4339 109 15 0.8 0.8 NUM ap-4339 109 16 1.2 1.2 NUM ap-4339 109 17 1.6 1.6 NUM ap-4339 109 18 2.0 2.0 NUM ap-4339 109 19 g g NOUN ap-4339 109 20 |i |i VERB ap-4339 109 21 m m PROPN ap-4339 109 22 e e NOUN ap-4339 109 23 | | ADV ap-4339 109 24 g g PROPN ap-4339 109 25 2 2 NUM ap-4339 109 26 e e NOUN ap-4339 110 1 x x X ap-4339 110 2 p p X ap-4339 110 3 [ [ X ap-4339 110 4 1 1 NUM ap-4339 110 5 / / SYM ap-4339 110 6 ( ( PUNCT ap-4339 110 7 2 2 NUM ap-4339 110 8 g g NOUN ap-4339 110 9 2 2 NUM ap-4339 110 10 ) ) PUNCT ap-4339 110 11 ] ] PUNCT ap-4339 110 12 figure figure NOUN ap-4339 110 13 1 1 NUM ap-4339 110 14 . . PUNCT ap-4339 111 1 present present ADJ ap-4339 111 2 calculation calculation NOUN ap-4339 111 3 of of ADP ap-4339 111 4 |=e|g2 |=e|g2 NOUN ap-4339 111 5 exp[1/(2g2 exp[1/(2g2 NOUN ap-4339 111 6 ) ) PUNCT ap-4339 111 7 ] ] PUNCT ap-4339 111 8 for for ADP ap-4339 111 9 the the DET ap-4339 111 10 oscillator oscillator NOUN ap-4339 111 11 ( ( PUNCT ap-4339 111 12 14 14 NUM ap-4339 111 13 ) ) PUNCT ap-4339 111 14 ( ( PUNCT ap-4339 111 15 solid solid ADJ ap-4339 111 16 line line NOUN ap-4339 111 17 ) ) PUNCT ap-4339 111 18 and and CCONJ ap-4339 111 19 the the DET ap-4339 111 20 results result NOUN ap-4339 111 21 of of ADP ap-4339 111 22 benassi benassi NOUN ap-4339 111 23 et et PROPN ap-4339 111 24 al[8 al[8 PROPN ap-4339 111 25 ] ] X ap-4339 111 26 ( ( PUNCT ap-4339 111 27 filled fill VERB ap-4339 111 28 circles circle NOUN ap-4339 111 29 ) ) PUNCT ap-4339 111 30 , , PUNCT ap-4339 111 31 killingbeck[9 killingbeck[9 PROPN ap-4339 111 32 ] ] X ap-4339 111 33 ( ( PUNCT ap-4339 111 34 crosses crosse NOUN ap-4339 111 35 ) ) PUNCT ap-4339 111 36 and and CCONJ ap-4339 111 37 fernández[6 fernández[6 NUM ap-4339 111 38 ] ] X ap-4339 111 39 ( ( PUNCT ap-4339 111 40 empty empty ADJ ap-4339 111 41 circles circle NOUN ap-4339 111 42 ) ) PUNCT ap-4339 111 43 . . PUNCT ap-4339 112 1 0.10 0.10 NUM ap-4339 112 2 0.15 0.15 NUM ap-4339 112 3 0.20 0.20 NUM ap-4339 112 4 0.25 0.25 NUM ap-4339 112 5 0.30 0.30 NUM ap-4339 112 6 -15 -15 PUNCT ap-4339 112 7 -10 -10 PUNCT ap-4339 112 8 -5 -5 NOUN ap-4339 112 9 0 0 PUNCT ap-4339 113 1 g g NOUN ap-4339 113 2 lo lo PROPN ap-4339 113 3 g g PROPN ap-4339 113 4 |i |i VERB ap-4339 113 5 m m VERB ap-4339 113 6 e e NOUN ap-4339 113 7 re re NOUN ap-4339 113 8 s s NOUN ap-4339 113 9 | | ADV ap-4339 113 10 lo lo PROPN ap-4339 113 11 g g NOUN ap-4339 113 12 |e |e PROPN ap-4339 113 13 b b PROPN ap-4339 113 14 s s X ap-4339 113 15 -r -r PUNCT ap-4339 113 16 e e X ap-4339 113 17 e e X ap-4339 113 18 re re X ap-4339 113 19 s s PROPN ap-4339 113 20 | | ADV ap-4339 113 21 figure figure NOUN ap-4339 113 22 2 2 NUM ap-4339 113 23 . . PUNCT ap-4339 113 24 log|=eres| log|=eres| NOUN ap-4339 113 25 ( ( PUNCT ap-4339 113 26 circles circle NOUN ap-4339 113 27 ) ) PUNCT ap-4339 113 28 and and CCONJ ap-4339 113 29 log|