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

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.

Minor changes and some additional references added in version 1

References in corpus (6)

• The Wigner distribution function for the one-dimensional parabose oscillator
• The su(2)_α Hahn oscillator and a discrete Hahn-Fourier transform
• A finite oscillator model related to sl(2|1)
• Discrete series representations for sl(2|1), Meixner polynomials and oscillator models
• Deformed su(1,1) Algebra as a Model for Quantum Oscillators
• sh(2/2) Superalgebra eigenstates and generalized supercoherent and supersqueezed states

Cited by in corpus (3)

• Exact solution of the position-dependent effective mass and angular frequency Schrödinger equation: harmonic oscillator model with quantized confinement parameter
• Exact solution of the position-dependent mass Schrödinger equation with the completely positive oscillator-shaped quantum well potential
• Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass