Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
Quantum Physics
2009-11-03 v1 High Energy Physics - Theory
Mathematical Physics
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigenfunctions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation versions of the Schr\"odinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.
Keywords
Cite
@article{arxiv.0802.1075,
title = {Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:0802.1075},
year = {2009}
}
Comments
46 pages, 2 figures