Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials
Copyright policy )Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials
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.
- Kurchatov Institute Russian Federation
- University of Wisconsin–Oshkosh United States
- University of Wisconsin–Stevens Point United States
- University of Wisconsin–Madison United States
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups and related algebraic methods applied to problems in quantum theory, Commutation relations and statistics as related to quantum mechanics (general), Al-Salam Carlitz polynomials
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Quantum groups and related algebraic methods applied to problems in quantum theory, Commutation relations and statistics as related to quantum mechanics (general), Al-Salam Carlitz polynomials
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