#### 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

#### 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