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タイトル: | Unified theory of exactly and quasiexactly solvable “discrete” quantum mechanics. I. Formalism |
著者: | Odake, Satoru Sasaki, Ryu |
著者名の別形: | 佐々木, 隆 |
キーワード: | eigenvalues and eigenfunctions polynomials quantum theory Schrodinger equation |
発行日: | Aug-2010 |
出版者: | American Institute of Physics |
誌名: | Journal of Mathematical Physics |
巻: | 51 |
号: | 8 |
論文番号: | 083502 |
抄録: | We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional “discrete” quantum mechanics, in which the Schrödinger 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. |
著作権等: | © 2010 American Institute of Physics |
URI: | http://hdl.handle.net/2433/131811 |
DOI(出版社版): | 10.1063/1.3458866 |
出現コレクション: | 学術雑誌掲載論文等 |
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