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Why are the energy levels of the quantum harmonic oscillator equally spaced?

 

作者: Antoine Royer,  

 

期刊: American Journal of Physics  （AIP Available online 1996）
卷期: Volume 64, issue 11  

页码: 1393-1399

 

ISSN:0002-9505

 

年代: 1996

 

DOI:10.1119/1.18364

 

出版商: American Association of Physics Teachers

 

关键词: HARMONIC OSCILLATORS;ENERGY LEVELS;PHASE SPACE;SYMMETRY;WIGNER DISTRIBUTION;HAMILTONIANS;ANGULAR MOMENTUM OPERATORS;ROTATIONAL INVARIANCE;03.65;01.65

 

数据来源: AIP

 

摘要:

The quantum harmonic oscillator has the unique property that its energy levels are equally spaced. This property is connected, via the Wigner function, to the circular symmetry of the Hamiltonian inphasespace, hence to the close relation between harmonic oscillations and rotations, very familiar at the classical level. We here have an example of a spectral regularity which is due to a symmetry in phase space, rather than in configuration space, as is more usual.

 

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