Bound States of a Finite Potential Well

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration shows the bound state energy levels and eigenfunctions for a square finite potential well defined by . The solutions are obtained by solving the time-independent Schrödinger equation in each region and requiring continuity of both the wavefunction and its first derivative. This leads to two transcendental equations, and , where . The graphical solutions to these equations give the bound state energy levels, shown on the left. The dependence of the energy levels and the corresponding eigenfunctions on well depth are shown on the right.

Contributed by: Porscha McRobbie and Eitan Geva (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

P. T. Tam, A Physicist's Guide to Mathematica, 2nd ed., Burlington, MA: Academic Press, 2008.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send