Calculating and visualizing the density of states for simple quantum mechanical systems

Author Info

Declan Mulhall, University of Scranton
Matthew J. Moelter, California Polytechnic State University - San Luis ObispoFollow

Recommended Citation

Published in American Journal of Physics, Volume 82, Issue 7, July 1, 2014, pages 665-673.

The definitive version is available at https://doi.org/10.1119/1.4867489.

Abstract

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations, we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the N-particle density of states arises from the single particle system it is based on.

Disciplines

Physics

Copyright

2014 American Institute of Physics.

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