The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
Mathematical Physics
2014-11-25 v2 math.MP
Representation Theory
Quantum Physics
Abstract
We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "the algebra of supersymmetric quantum mechanics", and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter gamma. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C_n with parameter gamma^2. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.
Keywords
Cite
@article{arxiv.1304.3295,
title = {The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials},
author = {E. I. Jafarov and J. Van der Jeugt},
journal= {arXiv preprint arXiv:1304.3295},
year = {2014}
}
Comments
Minor changes and some additional references added in version 1