Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism - Mathematical PhysicsReport as inadecuate




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Abstract: We present a simple recipe to construct exactly and quasi-exactly solvableHamiltonians in one-dimensional `discrete- quantum mechanics, in which theSchr\-{o}dinger equation is a difference equation. It reproduces all the knownones whose eigenfunctions consist of the Askey scheme of hypergeometricorthogonal polynomials of a continuous or a discrete variable. The recipe alsopredicts several new ones. An essential role is played by the sinusoidalcoordinate, which generates the closure relation and the Askey-Wilson algebratogether with the Hamiltonian. The relationship between the closure relationand the Askey-Wilson algebra is clarified.



Author: Satoru Odake, Ryu Sasaki

Source: https://arxiv.org/







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