Non-Hermitian two-dimensional harmonic oscillator in noncommutative phase-space

TL;DR

This paper explores a non-Hermitian two-dimensional harmonic oscillator within noncommutative phase-space, establishing a new PT-symmetry and analyzing its eigenvalue spectrum, extending previous work in the field.

Contribution

It introduces a novel PT-symmetry in noncommutative phase-space and demonstrates that the system's PT-regime remains unbroken, advancing understanding of non-Hermitian quantum systems.

Findings

Constructed a new PT-symmetry in NCPS

Proved the absence of PT-regime breaking

Computed the eigenvalue spectrum of the Hamiltonian

Abstract

In this paper, we extend the result of [Andreas Fring et al J. Phys. A 43, 345401 (2010)] in noncommutative phase-space (NCPS). We compute the non-Hermitian Hamiltonian of a harmonic oscillator in NCPS. We construct a new P T-symmetry in noncommutative phase-space and prove that the system does not possess a broken P T-regime. We then compute the eigenvalue spectrum of the non-Hermitian Hamiltonian of the system.