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

In this paper, we extend the result of [A. Fring et al. J. Phys. A 43 (2010) 345–401] in Noncommutative phase-space (NCPS). We compute the non-Hermitian Hamiltonian of a harmonic oscillator in NCPS. We construct a new [Formula: see text]-symmetry in NCPS and prove that the system does not possess a broken [Formula: see text]-regime. We then compute the eigenvalue spectrum of the non-Hermitian Hamiltonian of the system.