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

摘要

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 γ. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials Cn with parameter γ2. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.