A Fourier-Bessel expansion for solving radial Schrodinger equation in two dimensions
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, vol.61, no.5, pp.759-768, 1997 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 61 Issue: 5
- Publication Date: 1997
- Doi Number: 10.1002/(sici)1097-461x(1997)61:5<759::aid-qua3>3.0.co;2-v
- Journal Name: INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.759-768
- Middle East Technical University Affiliated: Yes
Abstract
The spectrum of the two-dimensional Schrodinger equation for polynomial oscillators bounded by infinitely high potentials, where the eigenvalue problem is defined on a finite interval r is an element of [0, L), is variationally studied. The wave function is expanded into a Fourier-Bessel series, and matrix elements in terms of integrals involving Bessel functions are evaluated analytically. Numerical results presented accurate to 30 digits show that, by the time L approaches a critical value, the tow-lying state energies behave almost as if the potentials were unbounded. The method is applicable to multiwell oscillators as well. (C) 1997 John Wiley & Sons, Inc.