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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 thenon-Hermitian Hamiltonian of a harmonic oscillator in NCPS. We construct a newP T-symmetry in noncommutative phase-space and prove that the system does notpossess a broken P T-regime. We then compute the eigenvalue spectrum of thenon-Hermitian Hamiltonian of the system.

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