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In the present paper, we study a two-dimensional harmonic oscillator in a constant magnetic field in noncommuting space. We use the following Hamiltonian [Formula: see text] with commutation relations [Formula: see text] and [Formula: see text]. The parameter λ expresses the presence of the magnetic field. We find the exact propagator of the system and the time evolution of the basic operators. We prove that the system is equivalent to a two-dimensional system where the operators of momentum and coordinates of the second dimension satisfy a deformed commutation relation [Formula: see text]. The deformation parameter, μ, depends on λ and θ, and is independent of the Hamiltonian. Finally, we investigate the thermodynamic properties of the system in Boltzmann statistics. We find the statistical density matrix and the partition function, which is equivalent to that of a two-dimensional harmonic oscillator with two deformed frequencies Ω1 and Ω2.

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In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator [Formula: see text] where λ,θ are real positive parameters, since the parameters α,β,m are for the general case complex. For the case α=1,β=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators [Formula: see text] in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex α=1,β=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case α,β,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters α,β the spectrum is real discrete and positive and the CPT symmetry is preserved. The general problem of deformed oscillator for non hermitian operators can be applied to the Solid State Physics.