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Spectrum generating functions for oscillators in Wigner's quantization

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Lievens S., Van der Jeugt J.

Banach Center Publications

2011

tom 93

nr 1

189-197

The n-dimensional (isotropic and non-isotropic) harmonic oscillator is studied as a Wigner quantum system. In particular, we focus on the energy spectrum of such systems. We show how to solve the compatibility conditions in terms of 𝔬𝔰𝔭(1|2n) generators, and also recall the solution in terms of 𝔤𝔩(1|n) generators. A method is described for determining a spectrum generating function for an element of the Cartan subalgebra when working with a representation of any Lie (super)algebra. Here, the character of the representation at hand plays a crucial role. This method is then applied to the n-dimensional isotropic harmonic oscillator, yielding explicit formulas for the energy eigenvalues and their multiplicities.

Ograniczanie wyników

1 Banach Center Publications

1 Lievens S.

1 Van der Jeugt J.

1 2011

Wyniki wyszukiwania

Spectrum generating functions for oscillators in Wigner's quantization