Finite q-oscillator

Details Finite q-oscillator Finite q-oscillator

2004-01-19

arxiv.org/abs/math-ph/0401035v1

Physics

Mathematical Physics

20 pages

Scientific paper

10.1088/0305-4470/37/21/005

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.

Affiliated with

Also associated with

No associations

Rating

Finite q-oscillator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finite q-oscillator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite q-oscillator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-569991