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arXiv · 1304.3295

The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials

E. I. Jafarov·J. Van der Jeugt
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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.

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E. I. Jafarov, J. Van der Jeugt. 2013-04-11. The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials. https://doi.org/10.1063/1.4824742

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