Distribution of quantum states in enclosures of finite size: II

Abstract

By making use of the modified form of Poisson's summation formula, we calculate the expression for the number of eigenstates, N(K), with eigenvalues [Formula: see text] of a particle in spherical and cylindrical enclosures of finite size, and with its wave-function subject to Dirichlet boundary conditions and Neumann boundary conditions at the walls of the container. We also obtain the oscillatory terms in addition to the important nonoscillatory terms already known and compare our results with the actual number of such states computed from the tables of the zeros of the relevant special mathematical functions. The inclusion of these oscillatory terms improves the accuracy of the expressions in all cases, especially in the case of the cylinder, where these are quite significant. Some possible applications of the results obtained here are also indicated.