One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-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): 33C45, 81T05
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics