TL;DR
This paper develops a method to analyze the energy levels of spheroidal quantum wells by using power series to solve boundary value problems, extending known results for spherical and cylindrical wells.
Contribution
It introduces an advanced approach for calculating low-lying energy levels in deep spheroidal quantum wells as a function of the spheroid's axes ratio.
Findings
Energy levels depend on spheroid axes ratio a/b
Results recover cylindrical and spherical wells in specific limits
Method provides accurate analysis for spheroidal quantum wells
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.
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Taxonomy
TopicsElectromagnetic Scattering and Analysis · Quantum and Classical Electrodynamics · Electromagnetic Simulation and Numerical Methods