Spectrum generating functions for oscillators in Wigner's quantization

• Autorzy: Stijn Lievens , Joris Van der Jeugt
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 81R05: Finite-dimensional groups and algebras motivated by physics and their representations
• 81R15: Operator algebra methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 93
• Numer: 1
• Strony: 189-197

Daty

wydano

2011

Twórcy

autor

Stijn Lievens

• Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Cornwallis Building, Kent CT2 7NF, United Kingdom

autor

Joris Van der Jeugt

• Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium

Identyfikatory

DOI

10.4064/bc93-0-15