Electron states and quantum transitions in a quantum ring on a sphere

TL;DR

This paper provides an analytical solution for electron states in a spherical quantum ring with angular confinement, revealing how symmetry breaking affects quantum transitions and selection rules.

Contribution

It introduces an exact analytical approach to solve the electron quantum problem on a spherical segment with rectangular potential walls, highlighting symmetry effects.

Findings

Solution reduces to hypergeometric equation

Quantum transition selection rules are violated

Symmetry breaking influences quantum states

Abstract

An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential of the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution of hypergeometric equation. As an application of the obtained results the quantum transitions in this system are discussed, and it is shown that the selection rule for quantum number l is removed due to the violation of spherical symmetry of the problem.