Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials
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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.
Mathematics Subject Classifications (1991)
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© Kluwer Academic Publishers 1993