Title

APPROXIMATING THE FINITE SQUARE-WELL WITH AN INFINITE WELL - ENERGIES AND EIGENFUNCTIONS

Document Type

Article

Publication Date

11-1-1991

Department

Physics and Astronomy

Abstract

Polynomial expansions are used to approximate the equations of the eigenvalues of the Schrodinger equation for a finite square potential well. The technique results in discrete, approximate eigenvalues which, it is shown, are identical to the corresponding eigenvalues of a wider, infinite well. The width of this infinite well is easy to calculate; indeed, the increase in width over that of the finite well is simply the original width divided by the well strength. The eigenfunctions of this wider, infinite well, which to first order has the same width for the ground state and all excited states, are also good approximations to the exact eigenfunctions of the finite well. These approximate eigenfunctions and eigenvalues are compared to accurate numeric calculations and to other approximations from the literature.

Publication Title

AMERICAN JOURNAL OF PHYSICS

Volume

59

Issue

11

First Page

1038

Last Page

1042