D:\sbornik\...\tpel.DVI


Mathematical Problems of Computer Science 36, 140{145, 2012.

N umer ical Solution of 1D Schr Äodinger E quation at

Adiabatically Changing P otential

A s h o t S . Ge vo r kya n 1;2 a n d Mis a k G. N a lb a n d ya n 1

1Institute for Informatics and Automation Problems, NAS of Armenia
2Joint Institute of Nuclear Research, 141980 Dubna, Moscow reg., Russia

e-mail g ashot@sci.am, habajyan@ipia.sci.am

Abstract

We study the eigenfunction and eigenvalue problem of 1D SchrÄodinger equation
with adiabatically changing along the reaction coordinate (external parameter) Mors
potential. As an example the 2D interaction potential of the collinear reactive collision
H ¡ H ¡ H is calculated which later is ¯tted by the generalized 2D Mors potential. It
is shown that the vibration state of body system are characterized by the set of ¯ve
orthonormalized wavefunctions and corresponding energies which are slowly changed
along the curve of the reaction coordinate. The mentioned problem is solved also with
taking into account rotation motion of bodies system. It is shown that the solution of
previous problem in this case is insigni¯cantly modi¯ed.

Keywords: Bodies system, eigenfunction and eigenvalue problem of SchrÄodinger
equation, ¯tting, Mors potential.

Refer ences

[1 ] A . S . Ge vo r kya n , G. G. B a lin t -K u r t i a n d G. N ym a n : N o ve l a lg o r it h m fo r s im u la t io n o f
3 D qu a n t u m r e a c t ive a t o m -d ia t o m s c a t t e r in g . P r o c e d ia CS 1 ( 1 ) , p p . 1 1 9 5 -1 2 0 , 2 0 1 0 .
1 0 .1 0 1 6 / j.p r o c s .2 0 1 0 .0 4 .1 3 3

[2 ] S . Flg g e , P ractical quantum mechanics I,. B e r lin , S p r in g e r , 1 9 7 4 .

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Àííîòàöèÿ

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