Abstract
Weyl's problem deals with the distribution of eigenvalues of the wave equation in a bounded domain. The integrated density of states counts the number of states up to a certain wavenumber and has important applications in nuclear physics, degenerate Fermi gases, blackbody radiation, and Bose-Einstein condensation. In the limit of large wavenumbers, the integrated density of states depends only on the volume of the domain and not on its shape. Corrections to this behaviour are well-known and depend on the surface area of the domain, its curvature and other features. We describe several computational projects that allow students to investigate this dependence for three different bounding domains – a rectangular box, a sphere and a circular cylinder. Quasi one- and two-dimensional systems can be analyzed by considering various limits. These projects could be incorporated into courses in quantum mechanics or statistical mechanics, or could stand alone in a computational physics course.
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