2023 Impact factor 4.2
Particles and Fields
Eur. Phys. J. C 6, 183-186
DOI 10.1007/s1005298000888

q-deformed Hermite polynomials in q-quantum mechanics

R. Hinterding1,2 - J. Wess1,2

1 Sektion Physik der Ludwig-Maximilians-Universität, Theresienstr. 37, D-80333 München, Germany
2 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, D-80805 München, Germany

Received: 5 March 1998 / Published online: 9 April 1998

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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