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rsta.2010.0262.pdf | 156.6 kB | Adobe PDF | 見る/開く |
タイトル: | Exactly and quasi-exactly solvable 'discrete' quantum mechanics. |
著者: | Sasaki, Ryu |
著者名の別形: | 佐々木, 隆 |
発行日: | 28-Mar-2011 |
出版者: | The Royal Society. |
誌名: | Philosophical transactions. Series A, Mathematical, physical, and engineering sciences |
巻: | 369 |
号: | 1939 |
開始ページ: | 1301 |
終了ページ: | 1318 |
抄録: | 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. |
著作権等: | © 2011 The Royal Society. 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。 This is not the published version. Please cite only the published version. |
URI: | http://hdl.handle.net/2433/140395 |
DOI(出版社版): | 10.1098/rsta.2010.0262 |
PubMed ID: | 21320918 |
出現コレクション: | 学術雑誌掲載論文等 |
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