Discrete quantum mechanics
Abstract
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrödinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrödinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasiexact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two new infinite families of orthogonal polynomials, the X_{ℓ} MeixnerPollaczek and the X_{ℓ} Meixner polynomials, are reported.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 September 2011
 DOI:
 10.1088/17518113/44/35/353001
 arXiv:
 arXiv:1104.0473
 Bibcode:
 2011JPhA...44I3001O
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Mathematics  Classical Analysis and ODEs;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Quantum Physics
 EPrint:
 61 pages, 1 figure. Comments and references added