Spherical quantum well

Abstract

Standard power series are used to construct and analyze angular and radial spheroidal functions, which are necessary for solving boundary value problems for Helmholtz equation in a spheroid. With an advanced approach the low-lying energy levels of a deep spheroidal quantum well are calculated as a function of the spheroid semiaxes ratio a/b. The well-known results for cylindrical and spherical wells are reproduced in the limits a/b >> 1, and a/b ~ 1, respectively.