New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics
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DOI[10.1093/ptep/ptx051]to the data of the same series
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- Material Type
- 記事
- Title
- Author/Editor
- Satoru Odake
- Publication, Distribution, etc.
- Publication Date
- 2017-05-18
- Publication Date (W3CDTF)
- 2017-05-18
- Periodical title
- Progress of Theoretical and Experimental Physics : PTEP
- No. or year of volume/issue
- 2017(5)
- Volume
- 2017(5)
- ISSN (Periodical Title)
- 2050-3911
- Text Language Code
- eng
- DOI
- 10.1093/ptep/ptx051
- Persistent ID (NDL)
- info:ndljp/pid/11375685
- Collection
- Collection (Materials For Handicapped People:1)
- Collection (particular)
- 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
- Acquisition Basis
- オンライン資料収集制度
- Date Accepted (W3CDTF)
- 2019-10-18T23:13:36+09:00
- Date Captured (W3CDTF)
- 2019-01-08
- Format (IMT)
- application/pdf
- Access Restrictions
- 国立国会図書館内限定公開
- Service for the Digitized Contents Transmission Service
- 図書館・個人送信対象外
- Availability of remote photoduplication service
- 可
- Periodical Title (URI)
- Periodical Title (Persistent ID (NDL))
- info:ndljp/pid/11375683
- Data Provider (Database)
- 国立国会図書館 : 国立国会図書館デジタルコレクション
- Summary, etc.
- 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.ArticlePROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS. 5:053A01 (2017)
- DOI
- 10.1093/ptep/ptx05110.48550/arxiv.1702.03078
- Access Restrictions
- インターネット公開
- Rights (production)
- © 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.
- Related Material (URI)
- Is Referenced By
- Recurrence relations of the multi-indexed orthogonal polynomials. VI. Meixner–Pollaczek and continuous Hahn types
- References
- Orthogonal polynomials from Hermitian matricesCasoratian identities for the Wilson and Askey-Wilson polynomialsRecurrence relations of the multi-indexed orthogonal polynomials. IIDiscrete quantum mechanics, (topical review)Crum's Theorem for 'Discrete' Quantum MechanicsAnother 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 polynomialsRecurrence relations of the multi-indexed orthogonal polynomials. IV. Closure relations and creation/annihilation operatorsTropical geometric interpretation of ultradiscrete singularity confinementMulti-indexed (<i>q</i>-)Racah polynomialsModification of Crum's Theorem for 'Discrete' Quantum MechanicsInfinitely many shape invariant potentials and new orthogonal polynomialsUnified theory of annihilation-creation operators for solvable ("discrete") quantum mechanicsExactly solvable 'discrete' quantum mechanics; Shape invariance, Heisenberg solutions, annihilation-creation operators and coherent statesEquivalences of the multi-indexed orthogonal polynomialsExtensions of solvable potentials with finitely many discrete eigenstatesExceptional (Xℓ) (q)-Racah polynomialsExactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomialsMulti-indexed Meixner and little<i>q</i>-Jacobi (Laguerre) polynomialsExact solution in the Heisenberg picture and annihilation-creation operatorsKrein-Adler transformations for shape-invariant potentials and pseudo virtual statesDual Christoffel TransformationsInfinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomialsA modification of Crum's methodMulti-indexed Jacobi polynomials and Maya diagramsA new recurrence formula for generic exceptional orthogonal polynomialsExceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformationsExceptional orthogonal polynomials, exactly solvable potentials and supersymmetryRational extensions of the quantum harmonic oscillator and exceptional Hermite polynomialsRecurrence relations for exceptional Hermite polynomialsASSOCIATED STURM-LIOUVILLE SYSTEMSExceptional Meixner and Laguerre orthogonal polynomialsTwo-step Darboux transformations and exceptional Laguerre polynomialsAn extended class of orthogonal polynomials defined by a Sturm–Liouville problemAn extension of Bochner’s problem: Exceptional invariant subspacesHigher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomialsÜber Sturm-Liouvillesche Polynomsysteme
- Data Provider (Database)
- 国立情報学研究所 : CiNii Research
- Original Data Provider (Database)
- 学術機関リポジトリデータベース雑誌記事索引データベースCrossrefCiNii Articles科学研究費助成事業データベースCrossref
- Bibliographic ID (NDL)
- 11375685
- NAID
- 120007100327