Two-body quantum mechanical problem on spheres

TL;DR

This paper investigates the quantum two-body problem on spheres, deriving differential equations for energy levels and explicitly calculating these levels for various potentials using representation theory.

Contribution

It introduces a new approach to solving the two-body quantum problem on spheres by applying recent representation theory results to derive and solve differential equations for energy levels.

Findings

Derived differential equations for energy levels on spheres.

Explicit calculations of energy levels for several potentials.

Applied representation theory to quantum mechanical problems on curved spaces.

Abstract

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.