The q-harmonic oscillator and an analogue of the Charlier polynomials
Copyright policy )The q-harmonic oscillator and an analogue of the Charlier polynomials
A model of a q-harmonic oscillator based on q-Charlier polynomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rational functions is observed.
- University of Wisconsin–Madison United States
- University of Wisconsin–Stevens Point United States
- University of Wisconsin–Oshkosh United States
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Coherent states, \(q\)-Charlier polynomials, Applications of basic hypergeometric functions, Quantum groups and related algebraic methods applied to problems in quantum theory
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Mathematics - Classical Analysis and ODEs, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Coherent states, \(q\)-Charlier polynomials, Applications of basic hypergeometric functions, Quantum groups and related algebraic methods applied to problems in quantum theory
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