Results 61 to 70 of about 7,854 (155)
Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states [PDF]
, 2008 Various examples of exactly solvable `discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states.
Odake, Satoru, Sasaki, Ryu
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Multi-indexed Wilson and Askey–Wilson polynomials [PDF]
, 2012 As the third stage of the project multi-indexed orthogonal polynomials, we present, in the framework of ‘discrete quantum mechanics’ with pure imaginary shifts in one dimension, the multi-indexed Wilson and Askey–Wilson polynomials.
S. Odake, R. Sasaki
semanticscholar +1 more source
The Universal Askey-Wilson Algebra and DAHA of Type (C_1^∨,C_1)
Symmetry, Integrability and Geometry: Methods and Applications, 2013 Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $Delta_q$ of AW(3) called the universal Askey-Wilson algebra.
Paul Terwilliger
doaj +1 more source
Multivariable Askey-Wilson Polynomials and Quantum Complex Grassmannians [PDF]
, 1996 We present a one-parameter family of constant solutions of the reflection equation and define a family of quantum complex Grassmannians endowed with a transitive action of the quantum unitary group.
M. Noumi, M. Dijkhuizen, T. Sugitani
semanticscholar +1 more source
Continuous −1$-1$ hypergeometric orthogonal polynomials
Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.Abstract The study of −1$-1$ orthogonal polynomials viewed as q→−1$q\rightarrow -1$ limits of the q$q$‐orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the −1$-1$ analog of the q$q$‐Askey scheme. A compendium of the properties of all the continuous −1$-1$ hypergeometric polynomials and their connections is ...
Jonathan Pelletier +2 more
wiley +1 more source
Wilson function transforms related to Racah coefficients
, 2005 The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series.
A.N. Kirillov +37 more
core +2 more sources
, 2005 The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite ...
Odake, S., Sasaki, R.
core +2 more sources
Nonnegative Linearization and Quadratic Transformation of Askey-Wilson Polynomials [PDF]
Canadian Mathematical Bulletin, 1996 AbstractNonnegative product linearization of the Askey-Wilson polynomials is shown for a wide range of parameters. As a corollary we obtain Rahman's result on the continuous q-Jacobi polynomials with α ≥ β > — 1 and α + β + 1 ≥ 0.
Ryszard Szwarc
openalex +2 more sources
On Some Limit Cases of Askey–Wilson Polynomials
Journal of Approximation Theory, 1998 The authors derive the classical orthogonality relations and norm evaluations for the \(q\)-Racah and \(q\)-Jacobi polynomials by taking limits in the orthogonality relations and norm evaluations for the Askey-Wilson polynomials [\textit{R. Askey} and \textit{J. Wilson}, Mem. Am. Math. Soc. 54, No. 319, 1-55 (1985; Zbl 0572.33012)].
Stokman, J.V., Koornwinder, T.H.
openaire +4 more sources
Orthogonal Polynomials of Askey-Wilson Type
, 2022 26 ...
Ismail, Mourad E. H. +2 more
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