Representations of the Schrodinger algebra and Appell systems

Details Representations of the Schrodinger algebra and Appell systems Representations of the Schrodinger algebra and Appell systems

2000-08-24

arxiv.org/abs/math-ph/0008035v1

Fortschritte der Physik, vol. 52, Issue 4, pp.343-359, 2004

Physics

Mathematical Physics

23 pages, LaTeX

Scientific paper

We investigate the structure of the Schrodinger algebra and its representations in a Fock space realized in terms of canonical Appell systems. Generalized coherent states are used in the construction of a Hilbert space of functions on which certain commuting elements act as self-adjoint operators. This yields a probabilistic interpretation of these operators as random variables. An interesting feature is how the structure of the Lie algebra is reflected in the probability density function. A Leibniz function and orthogonal basis for the Hilbert space is found. Then Appell systems connected with certain evolution equations, analogs of the classical heat equation, on this algebra are computed.

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