2021-10-17T12:14:22Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000118382021-09-02T06:13:14Z1169:1170Unified theory of exactly and quasiexactly solvable "discrete" quantum mechanics. I. FormalismOdake, SatoruSasaki, RyuANNIHILATION-CREATION OPERATORSORTHOGONAL POLYNOMIALSPREPOTENTIAL APPROACHSUPERSYMMETRYPOTENTIALSDERIVATIONSYMMETRYEQUATIONWe present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional "discrete" quantum mechanics, in which the Schrodinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey Wilson algebra is clarified. (C) 2010 American Institute of Physics. [doi:10.1063/1.3458866]ArticleJOURNAL OF MATHEMATICAL PHYSICS. 51(8):083502 (2010)journal articleAMER INST PHYSICS2010-08application/pdfJOURNAL OF MATHEMATICAL PHYSICS8510022-2488AA00701758https://soar-ir.repo.nii.ac.jp/record/11838/files/Unified_theory_exactly_quasiexactly_solvable.pdfeng10.1063/1.3458866https://doi.org/10.1063/1.3458866Copyright © 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. along with the following message: The following article appeared in J. Math. Phys. 51, 083502 (2010) and may be found at https://doi.org/10.1063/1.3458866 .