(Quasi) exactly solvable `Discrete' quantum mechanics
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Discrete Integrable Systems
This talk is based on the collaboration with Ryu Sasaki.
`Discrete’ quantum mechanics is a quantum mechanical system whose Schr”{o}dinger equation is a difference equation instead of differential in ordinary quantum mechanics.
We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in onedimensional `discrete’ quantum mechanics.
It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable.
An essential role is played by the sinusoidal coordinate, which generates the closure relation and the AskeyWilson algebra together with the Hamiltonian.
We also present the Crum’s Theorem for `discrete’ quantum mechanics.
This talk is part of the Isaac Newton Institute Seminar Series series.
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