Two dimensional non-Hermitian harmonic oscillator: coherent states

TL;DR

This paper explores a two-dimensional non-Hermitian harmonic oscillator with real eigenvalues and constructs its coherent states, analyzing how non-Hermiticity affects probability densities.

Contribution

It introduces a novel two-dimensional non-Hermitian harmonic oscillator with space and time reflection symmetry and constructs its coherent states.

Findings

Eigenvalues are real despite non-Hermiticity.

Constructed coherent states from superpositions of eigenfunctions.

Analyzed modifications in probability densities due to non-Hermitian properties.

Abstract

In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schr\"odinger equation yields real eigenvalues with complex eigenfunctions. We also construct the coherent state of the system by using a superposition of 12 eigenfunctions. Using the complex correspondence principle for the probability density we investigate the possible modifications in the probability densities due to the non-Hermitian aspect of the Hamiltonian.