Spectrum generating functions for oscillators in Wigner's quantization

Stijn Lievens, and Joris Van der Jeugt. "Spectrum generating functions for oscillators in Wigner's quantization." Banach Center Publications 93.1 (2011): 189-197. <http://eudml.org/doc/281910>.

@article{StijnLievens2011,
abstract = {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.},
author = {Stijn Lievens, Joris Van der Jeugt},
journal = {Banach Center Publications},
keywords = {Wigner quantization; -dimensional oscillator; spectrum},
language = {eng},
number = {1},
pages = {189-197},
title = {Spectrum generating functions for oscillators in Wigner's quantization},
url = {http://eudml.org/doc/281910},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Stijn Lievens
AU - Joris Van der Jeugt
TI - Spectrum generating functions for oscillators in Wigner's quantization
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 189
EP - 197
AB - 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.
LA - eng
KW - Wigner quantization; -dimensional oscillator; spectrum
UR - http://eudml.org/doc/281910
ER -