Exactly solvable ‘ discrete ’ quantum mechanics ; shape invariance , Heisenberg solutions , annihilation - creation operators and coherent states
نویسنده
چکیده
Various examples of exactly solvable ‘discrete’ quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilationcreation 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 Schrödinger equation. Various reductions (restrictions) of the symmetry algebra of the Askey-Wilson system are explored in detail.
منابع مشابه
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly...
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تاریخ انتشار 2008