How the quantum ring shape influences its energy spectrum

TL;DR

This paper introduces a new method for modeling the energy spectrum of quantum rings with various shapes using oblate spheroidal coordinates, revealing how shape influences spectral properties.

Contribution

It presents a novel approach based on separation of variables in spheroidal coordinates to analyze quantum ring spectra for different geometries.

Findings

Spectrum depends on ring shape, showing parabolic or non-parabolic behavior.

Model calculates ground and excited state spectra.

Shape influences magnetic quantum number dependence.

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