Meixner Oscillators
arXiv:math-ph/9807035
Abstract
Meixner oscillators have a ground state and an `energy' spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it difference} operator. Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the Sommerfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and their continuous weight function. We construct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,). The reproducing kernel for the wavefunctions of these models is also found.
18 pages, LaTex, published in "Revista Mexicana de Fisica", V.44, N3, pp. 235-244, 1998
Cited by in corpus (7)
- Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra
- Finite q-oscillator
- A superintegrable discrete oscillator and two-variable Meixner polynomials
- The Fourier U(2) Group and Separation of Discrete Variables
- Creation and Annihilation Operators for Orthogonal Polynomials of Continuous and Discrete Variables
- Factorizacion of the hypergeometric-type difference equation on the uniform lattice
- Coherent States for generalized oscillator with finite-dimensional Hilbert space