The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
Journal Article
·
· Journal of Mathematical Physics
- Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent (Belgium)
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 C{sub n} with parameter γ{sup 2}. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.
- OSTI ID:
- 22217891
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 10; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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