From the Philosophical Transactions of The Royal Society
Cambridge University Press eBooksPublished 3 November 2011
William Parsons
Citations1,079
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Keywords
Arts and Humanities
Physics ReportsSupersymmetry and quantum mechanics
2,768 Citations1995Fred Cooper, Avinash Khare +1 more
arXiv (Cornell University)The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
1,233 Citations1996Roelof Koekoek, René F. Swarttouw
Bulletin of the London Mathematical SocietySPECIAL FUNCTIONS (Encyclopedia of Mathematics and its Applications 71)
664 Citations2001Frits Beukers
Quasi-exactly solvable models in quantum mechanics
473 Citations2017A.G. Ushveridze
Physics Letters BInfinitely many shape invariant potentials and new orthogonal polynomials
246 Citations2009Satoru Odake, Ryu Sasaki
Theoretical and Mathematical Physics“Hidden symmetry” of Askey-Wilson polynomials
243 Citations1991Alexei Zhedanov
Annals of PhysicsMutual integrability, quadratic algebras, and dynamical symmetry
183 Citations1992Ya.I. Granovskii, I.M Lutzenko +1 more
Physics Letters BAnother 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
147 Citations2010Satoru Odake, Ryu Sasaki
Physical Review LettersBethe-ansatz for the Bloch electron in magnetic field
136 Citations1994P. Wiegmann, A. Zabrodin
The approach allows us to express the spectrum and the Bloch function as solutions of the Bethe-ansatz equations typical for completely integrable quantum systems.
Journal of Mathematical PhysicsOrthogonal polynomials from Hermitian matrices
80 Citations2008Satoru Odake, Ryu Sasaki
Journal of Mathematical PhysicsUnified theory of annihilation-creation operators for solvable (“discrete”) quantum mechanics
76 Citations2006Satoru Odake, Ryu Sasaki
Physics Letters BInfinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials
74 Citations2009Satoru Odake, Ryu Sasaki
Institutional Repositories DataBase (IRDB)Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
68 Citations2010Satoru Odake, Ryu Sasaki
Journal of Physics A Mathematical and GeneralQuantum Inozemtsev model, quasi-exact solvability and 𝒩-fold supersymmetry
53 Citations2001Ryu Sasaki, Kanehisa Takasaki
arXiv (Cornell University)Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials
50 Citations2004Paul Terwilliger
Progress of Theoretical PhysicsModification of Crum's Theorem for 'Discrete' Quantum Mechanics
43 Citations2010Leonor García-Gutierrez, Satoru Odake +1 more
Symmetry Integrability and Geometry Methods and ApplicationsZhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
43 Citations2008Tom H. Koornwinder
Physics Letters BExact solution in the Heisenberg picture and annihilation–creation operators
41 Citations2006Satoru Odake, Ryu Sasaki
SOAR (Shinshu University)1 Crum’s Theorem for ‘Discrete ’ Quantum Mechanics
39 Citations2009Satoru Odake, Ryu Sasaki
Journal of Physics A Mathematical and TheoreticalExceptional Askey–Wilson-type polynomials through Darboux–Crum transformations
29 Citations2010Satoru Odake, Ryu Sasaki
Methods and Applications of AnalysisSpectral transformations and generalized Pollaczek polynomials
25 Citations1999Oksana Yermolayeva, Alexei Zhedanov
Proceedings of the Royal Society of London A Mathematical and Physical SciencesGeometric theory of local and non-local conservation laws for the sine-Gordon equation
24 Citations1981Ryu Sasaki, R. Bullough
Proceedings of the Royal Society of London A Mathematical and Physical SciencesGeometric approach to soliton equations
16 Citations1980R. Sakaki
Journal of Nonlinear Mathematical PhysicsNew Quasi-Exactly Solvable Difference Equation
12 Citations2008Ryu Sasaki
Lecture notes in physicsGeometry of the akns — ZS inverse scattering scheme
9 Citations2008Ryu Sasaki, R. Bullough
