How the quantum ring shape influences its energy spectrum

Abstract

We propose a new approach for modeling the quantum ring single particle energy spectrum. The approach is based on separation of variables in the Schr\"odinger equation in oblate spheroidal coordinates. We consider a model of a spheroidal quantum ring with infinite walls. Our simple model allowed us to study the spectra for quantum rings of different shapes. The spectrum is calculated for the ground and several excited states and the ring shape dependence of the spectrum is demonstrated. The spectrum can demonstrate parabolic or non-parabolic dependence on the magnetic quantum number for different shapes of the ring