Energy Spectra of the Harmonic Oscillator in a Generalized Noncommutative Phase Space of Arbitrary Dimension

We use the invariant eigen-operator method to study the higher-dimensional harmonic oscillator in a type of generalized noncommutative phase space, and obtain the explicit expression of the energy spectra of the noncommutative harmonic oscillator in arbitrary dimension. It is found that the energy spectra of the higher-dimensional noncommutative harmonic oscillator are equal to the sum of the energy spectra of some 1D harmonic oscillators and some 2D noncommutative harmonic oscillators. We believe that the properties of the harmonic oscillator may reflect some essence of the noncommutative phase space.