Energy levels and wave functions of a particle confined in the potential well of ellipsoidal shape

Author: Tamaz Kereselidze
Co-authors: Tamar Tchelidze
Keywords: Ellipsoidal potential, Nanoparticles, Energy levels
Annotation:

A charged particle (electron or hole) confined in the potential well of strongly prolate ellipsoidal shape is considered. The effective-mass Schrödinger equation is solved in prolate spheroidal coordinates and asymptotically exact expressions for the energy spectrum and wave functions are derived. The obtained energy spectrum is in good qualitative and quantitative agreement with the spectrum obtained earlier by numerical solution of the problem in spheroidal coordinates.