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Energy Spectra of the Harmonic Oscillator in a Generalized Noncommutative Phase Space of Arbitrary Dimension |
| LIN Bing-Sheng1**, HENG Tai-Hua2
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1 School of Mathematical Sciences, Capital Normal University, Beijing 100048
2 School of Physics and Material Science, Anhui University, Hefei 230039
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| Cite this article: |
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LIN Bing-Sheng, HENG Tai-Hua 2011 Chin. Phys. Lett. 28 070303 |
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Abstract 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.
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| Keywords:
03.65.Fd
02.40.Gh
03.65.Ta
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Received: 20 March 2011
Published: 29 June 2011
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| PACS: |
03.65.Fd
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(Algebraic methods)
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02.40.Gh
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(Noncommutative geometry)
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03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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