A quantum particle on the surface of a box

Abstract

A particle was constrained to move freely on the surface of a box. The density of states was calculated for different box sizes. It was shown that when one edge is significantly larger than another, the ground state energy becomes significantly smaller. By varying the lengths of the edges, it is possible to have spread or clustered allowed energy states. In the limit that the box approaches a line, the allowed energies include the allowed energies of the infinite square well.