# Numerical Solution of 1D Schrödinger Equation at Adiabatically Changing Potential

## Keywords:

Bodies system, eigenfunction and eigenvalue problem of Schrödingerr equation, fitting, Mors potential## Abstract

We study the eigenfunction and eigenvalue problem of 1D Schrödinger 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 fitted by the generalized 2D Mors potential. It is shown that the vibration state of body system are characterized by the set of five orthonormalized wave functions 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 insignificantly modified.

## References

A.S. Gevorkyan, G.G. Balint-Kurti and G. Nyman: Novel algorithm for simulation of 3D quantum reactive atom-diatom scattering. Procedia CS1 (1), pp. 1195-120, 2010.10.1016/j.procs.2010.04.133

S. Flgge, Practical quantum mechanics I,. Berlin, Springer, 1974.

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*Mathematical Problems of Computer Science*,

*36*, 140–145. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/277

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