Two-dimensional non-Hermitian harmonic oscillator: coherent states

Abstract

In this study, we introduce a two-dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time-independent Schrodinger 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.