Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials |
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Authors: | R. Askey S. K. Suslov |
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Affiliation: | (1) Department of Mathematics, University of Wisconsin, 53706 Madison, WI, USA;(2) Russian Scientific Center Kurchatov Institute , 123182 Moscow, Russia |
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Abstract: | One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed. |
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Keywords: | 33C45 81T05 |
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