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arXiv:math/9803050 · The European Physical Journal C

$q$ -deformed Hermite polynomials in $q$ -quantum mechanics

R. Hinterding, J. Wess

Published Jan 1, 1999• 8 citations
arXivHTMLPDF
DOI
10.1007/s100529800888

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Europhysics Letters (EPL)•Mar 1, 2023•10 citations
qqq -deformed Hermite polynomials in qqq -quantum mechanics
Abstract We discuss quantum mechanical systems with Dunkl derivatives by constructing the Dunkl-Heisenberg relation in the momentum representation by means of the reflection operator for momentum and we obtain the corresponding position quantum eigenfunction. We examine the one-dimensional Dunkl oscillator in the momentum space in terms of ν -deformed Hermite polynomials. We obtain the energy levels as well as the ground-state and excited wave functions in terms of the ν -deformed Hermite polynomials. We also describe some properties of the ν -deformed Hermite polynomials. We apply the method to the construction of coherent states.