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 ∈ [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 thirty 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 multi-well oscillators as well.
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