Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states

摘要

Various examples of exactly solvable `discrete' quantum mechanics areexplored explicitly with emphasis on shape invariance, Heisenberg operatorsolutions, annihilation-creation operators, the dynamical symmetry algebras andcoherent states. The eigenfunctions are the (q-)Askey-scheme of hypergeometricorthogonal polynomials satisfying difference equation versions of theSchr\"odinger equation. Various reductions (restrictions) of the symmetryalgebra of the Askey-Wilson system are explored in detail.