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Title: Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Authors: Sasaki, Ryu
Author's alias: 佐々木, 隆
Issue Date: 28-Mar-2011
Publisher: The Royal Society.
Journal title: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Volume: 369
Issue: 1939
Start page: 1301
End page: 1318
Abstract: 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 solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Rights: © 2011 The Royal Society.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.1098/rsta.2010.0262
PubMed ID: 21320918
Appears in Collections:Journal Articles

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