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We investigate an algebraic model for the quantum oscillator based upon theLie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or "thealgebra of supersymmetric quantum mechanics", and its Fock representation. Themodel offers some freedom in the choice of a position and a momentum operator,leading to a free model parameter gamma. Using the technique of Jacobimatrices, we determine the spectrum of the position operator, and show that itswavefunctions are related to Charlier polynomials C_n with parameter gamma^2.Some properties of these wavefunctions are discussed, as well as some otherproperties of the current oscillator model.

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