Finiteq-oscillator
| Autor: | Anatoliy U. Klimyk, Kurt Bernardo Wolf, Natig M. Atakishiyev |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Physics
Time evolution FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Observable Mathematical Physics (math-ph) Classical limit Schrödinger equation symbols.namesake Lie algebra symbols Coherent states Hamiltonian (quantum mechanics) Mathematical Physics Harmonic oscillator Mathematical physics |
| Zdroj: | Journal of Physics A: Mathematical and General. 37:5569-5587 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/37/21/005 |
| Popis: | The finite q-oscillator is a model that obeys the dynamics of the harmonic oscillator, with the operators of position, momentum and Hamiltonian being functions of elements of the q-algebra su_q(2). The spectrum of position in this discrete system, in a fixed representation j, consists of 2j+1 "sensor"-points x_s=(1/2)[2s]_q, s=-j, -j+1,..., j, and similarly for the momentum observable. The spectrum of energies is finite and equally spaced, so the system supports coherent states. The wave functions involve dual q-Kravchuk polynomials, which are solutions to a finite-difference Schrodinger equation. Time evolution (times a phase) defines the fractional Fourier-q-Kravchuk transform. In the classical limit q -> 1 we recover the finite oscillator Lie algebra, the N=2j -> infinity limit returns the Macfarlane-Biedenharn q-oscillator and both limits contract the generators to the standard quantum-mechanical oscillator. 20 pages |
| Databáze: | OpenAIRE |
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