A Fourier-Bessel expansion for solving radial Schr�dinger equation in two dimensions

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