A Fourier-Bessel expansion for solving radial Schrödinger equation in two dimensions

✍ Scribed by H. Taşeli; A. Zafer

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 161 KB
• Volume: 61
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)61:5<759::aid-qua3>3.0.co;2-v

✦ Synopsis

The spectrum of the two-dimensional Schrodinger equation for polynomial oscillators bounded by infinitely high potentials, where the eigenvalue problem is defined on a w . finite interval r g 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 low-lying state energies behave almost as if the potentials were unbounded. The method is applicable to multiwell oscillators as well.