New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics

• 資料種別: 記事
• タイトル: New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics
• 著者・編者: Satoru Odake
• 出版事項: 日本 : Oxford University Press
• 出版年月日等: 2017-05-18
• 出版年（W3CDTF）: 2017-05-18
• タイトル（掲載誌）: Progress of Theoretical and Experimental Physics : PTEP
• 巻号年月日等（掲載誌）: 2017(5)
• 掲載巻: 2017(5)
• ISSN（掲載誌）: 2050-3911
• 本文の言語コード: eng
• DOI: 10.1093/ptep/ptx051; https://doi.org/10.1093/ptep/ptx051
• 国立国会図書館永続的識別子: info:ndljp/pid/11375685; https://dl.ndl.go.jp/pid/11375685
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• コレクション（個別）: 国立国会図書館デジタルコレクション > 電子書籍・電子雑誌 > その他; https://dl.ndl.go.jp/collections/B00035
• 収集根拠: オンライン資料収集制度
• 受理日（W3CDTF）: 2019-10-18T23:13:36+09:00
• 保存日（W3CDTF）: 2019-01-08
• 記録形式（IMT）: application/pdf
• オンライン閲覧公開範囲: 国立国会図書館内限定公開
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• 遠隔複写可否（NDL）: 可
• 掲載誌（URI）: https://academic.oup.com/ptep/article/2017/5/053A01/3833778
• 掲載誌（国立国会図書館永続的識別子）: info:ndljp/pid/11375683; https://dl.ndl.go.jp/pid/11375683
• 連携機関・データベース: 国立国会図書館 : 国立国会図書館デジタルコレクション; https://dl.ndl.go.jp

• 要約等: Multi-indexed orthogonal polynomials (the Meixner, little q-Jacobi (Laguerre), (q-) Racah, Wilson, and Askey-Wilson types) satisfying second-order difference equations were constructed in discrete quantum mechanics. They are polynomials in sinusoidal coordinates eta(x) (x is the coordinate of the quantum system) and are expressed in terms of Casorati determinants whose matrix elements are functions of x at various points. By using shape-invariance properties, we derive various equivalent determinant expressions, especially those whose matrix elements are functions of the same point x. Except for the (q-) Racah case, they can be expressed in terms of eta only, without explicit x-dependence.; Article; PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS. 5:053A01 (2017)
• DOI: 10.1093/ptep/ptx051; https://doi.org/10.1093/ptep/ptx051; 10.48550/arxiv.1702.03078; https://doi.org/10.48550/arxiv.1702.03078
• オンライン閲覧公開範囲: インターネット公開
• 著作権情報: © The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan. / This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
• 関連情報（URI）: http://hdl.handle.net/10091/00020585; https://soar-ir.repo.nii.ac.jp/records/19824; http://id.ndl.go.jp/digimeta/11375685; https://dl.ndl.go.jp/pid/11375685; http://academic.oup.com/ptep/article-pdf/2017/5/053A01/17213466/ptx051.pdf
• 参照: Recurrence relations of the multi-indexed orthogonal polynomials. VI. Meixner–Pollaczek and continuous Hahn types; https://cir.nii.ac.jp/crid/1360290617827847040
• 参照: Orthogonal polynomials from Hermitian matrices; https://cir.nii.ac.jp/crid/1050001338921931776; Casoratian identities for the Wilson and Askey-Wilson polynomials; https://cir.nii.ac.jp/crid/1050001338921932928; Recurrence relations of the multi-indexed orthogonal polynomials. II; https://cir.nii.ac.jp/crid/1050001338921940224; Discrete quantum mechanics, (topical review); https://cir.nii.ac.jp/crid/1050001338921947008; Crum's Theorem for 'Discrete' Quantum Mechanics; https://cir.nii.ac.jp/crid/1050001338921948160; Another set of infinitely many exceptional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>ℓ</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math> Laguerre polynomials; https://cir.nii.ac.jp/crid/1050001338921968512; Recurrence relations of the multi-indexed orthogonal polynomials. IV. Closure relations and creation/annihilation operators; https://cir.nii.ac.jp/crid/1050001338927223680; Tropical geometric interpretation of ultradiscrete singularity confinement; https://cir.nii.ac.jp/crid/1050282813898656640; Multi-indexed (<i>q</i>-)Racah polynomials; https://cir.nii.ac.jp/crid/1050282813898657792; Modification of Crum's Theorem for 'Discrete' Quantum Mechanics; https://cir.nii.ac.jp/crid/1050282813898658816; Infinitely many shape invariant potentials and new orthogonal polynomials; https://cir.nii.ac.jp/crid/1050282813898678784; Unified theory of annihilation-creation operators for solvable ("discrete") quantum mechanics; https://cir.nii.ac.jp/crid/1050564288875351808; Exactly solvable 'discrete' quantum mechanics; Shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states; https://cir.nii.ac.jp/crid/1050564288875352960; Equivalences of the multi-indexed orthogonal polynomials; https://cir.nii.ac.jp/crid/1050564288875360768; Extensions of solvable potentials with finitely many discrete eigenstates; https://cir.nii.ac.jp/crid/1050564288875368064; Exceptional (Xℓ) (q)-Racah polynomials; https://cir.nii.ac.jp/crid/1050564288875369216; Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials; https://cir.nii.ac.jp/crid/1050564288875390080; Multi-indexed Meixner and little<i>q</i>-Jacobi (Laguerre) polynomials; https://cir.nii.ac.jp/crid/1050564288880645504; Exact solution in the Heisenberg picture and annihilation-creation operators; https://cir.nii.ac.jp/crid/1050845763852061952; Krein-Adler transformations for shape-invariant potentials and pseudo virtual states; https://cir.nii.ac.jp/crid/1050845763852078464; Dual Christoffel Transformations; https://cir.nii.ac.jp/crid/1050845763852079488; Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials; https://cir.nii.ac.jp/crid/1050845763852100096; A modification of Crum's method; https://cir.nii.ac.jp/crid/1360011143835445888; Multi-indexed Jacobi polynomials and Maya diagrams; https://cir.nii.ac.jp/crid/1360285708889229696; A new recurrence formula for generic exceptional orthogonal polynomials; https://cir.nii.ac.jp/crid/1360285708890482304; Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations; https://cir.nii.ac.jp/crid/1360285709429918848; Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry; https://cir.nii.ac.jp/crid/1360855571485644800; Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials; https://cir.nii.ac.jp/crid/1361981469267206400; Recurrence relations for exceptional Hermite polynomials; https://cir.nii.ac.jp/crid/1362262945497774336; ASSOCIATED STURM-LIOUVILLE SYSTEMS; https://cir.nii.ac.jp/crid/1362262946395276160; Exceptional Meixner and Laguerre orthogonal polynomials; https://cir.nii.ac.jp/crid/1362544420479209088; Two-step Darboux transformations and exceptional Laguerre polynomials; https://cir.nii.ac.jp/crid/1362825894148044544; An extended class of orthogonal polynomials defined by a Sturm–Liouville problem; https://cir.nii.ac.jp/crid/1363388846214544896; An extension of Bochner’s problem: Exceptional invariant subspaces; https://cir.nii.ac.jp/crid/1363951794789943168; Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials; https://cir.nii.ac.jp/crid/1363951795207454208; Über Sturm-Liouvillesche Polynomsysteme; https://cir.nii.ac.jp/crid/1363951795966678272
• 連携機関・データベース: 国立情報学研究所 : CiNii Research; https://cir.nii.ac.jp/
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• 書誌ID（NDLBibID）: 11375685; http://id.ndl.go.jp/bib/11375685
• NII論文ID: 120007100327