Approximating the Finite Square Well with an Infinite Well: Energies and Eigenfunctions
Document Type
Article
Publication Date
11-1-1991
Department
Physics and Astronomy
School
Mathematics and Natural Sciences
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
Recommended Citation
Barker, B. I.,
Rayborn, G. H.,
Ioup, J. W.,
Ioup, G. E.
(1991). Approximating the Finite Square Well with an Infinite Well: Energies and Eigenfunctions. American Journal of Physics, 59(11), 1038-1042.
Available at: https://aquila.usm.edu/fac_pubs/7098