Perturbation Theory on the Non-Commutative Plane with a Singular Potential

TL;DR

This paper investigates the energy spectrum of a non-relativistic particle in a noncommutative plane with a singular potential, revealing non-analytic behavior in the noncommutativity parameter.

Contribution

It provides a detailed analysis of the spectral properties of a particle under a singular potential in noncommutative geometry, highlighting non-analytic dependence on the noncommutativity parameter.

Findings

Energy spectrum is non-analytic in the noncommutativity parameter.

The singular potential significantly affects the spectral properties.

The study advances understanding of quantum systems in noncommutative spaces.

Abstract

In this article we study the problem of a non-relativistic particle in the presence of a singular potential in the noncommutative plane. The potential contains a term proportional to $1/R^2$, where $R^2$ is the squared distance to the origin in the noncommutative plane. We find that the spectrum of energies is non analytic in the noncommutativity parameter $\theta$.