Multiplicity of the lowest eigenvalue of non-commuatative harmonic oscillators

TL;DR

This paper investigates the multiplicity of the lowest eigenvalue of non-commutative harmonic oscillators, establishing conditions under which this eigenvalue is simple, thus contributing to the spectral theory of such operators.

Contribution

The paper provides new conditions ensuring the simplicity of the lowest eigenvalue for non-commutative harmonic oscillators.

Findings

The lowest eigenvalue is simple within certain parameter regions.

Conditions for eigenvalue simplicity are explicitly characterized.

Results advance understanding of spectral properties of non-commutative oscillators.

Abstract

The multiplicity of the lowest eigenvalue E of the so-called non-commutative harmonic oscillator Q(\alpha,\beta) is studied. It is shown that E is simple for \alpha and \beta in some region.