q-deformed Hermite Polynomials in q-Quantum Mechanics

Details q-deformed Hermite Polynomials in q-Quantum Mechanics q-deformed Hermite Polynomials in q-Quantum Mechanics

1998-03-12

arxiv.org/abs/math/9803050v1

Mathematics

Quantum Algebra

latex, 8 pages, no figures. accepted for publication in European Journal of Physics C

Scientific paper

10.1007/s100529800888

The q-special functions appear naturally in q-deformed quantum mechanics and
both sides profit from this fact. Here we study the relation between the
q-deformed harmonic oscillator and the q-Hermite polynomials. We discuss:
recursion formula, generating function, Christoffel-Darboux identity,
orthogonality relations and the moment functional.

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