Perturbations around the zeros of classical orthogonal polynomials

DOI10.1063/1.4918707zbMath1322.81038arXiv1411.3045OpenAlexW3102604454MaRDI QIDQ5250072

Ryu Sasaki

Publication date: 15 May 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3045

zbMATH Keywords

zerosperturbationsclassical orthogonal polynomialstime dependent Schrödinger equationsRacah and \(q\)-Racah polynomialsWilson and Askey-Wilson polynomials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Classical hypergeometric functions, ({}_2F_1) (33C05) Linear Diophantine equations (11D04) Linear equations (linear algebraic aspects) (15A06) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (6)

Generalized pseudospectral method and zeros of orthogonal polynomials ⋮ Properties of the zeros of generalized basic hypergeometric polynomials ⋮ Discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts ⋮ Discrete orthogonality relations for multi-indexed Laguerre and Jacobi polynomials ⋮ New Properties of the Zeros of Krall Polynomials ⋮ Finite-dimensional representations of difference operators and the identification of remarkable matrices

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Properties of the zeros of the polynomials belonging to the Askey scheme
• Properties of the zeros of the polynomials belonging to the \(q\)-Askey scheme
• Exact solution in the Heisenberg picture and annihilation-creation operators
• \(q\)-oscillator from the \(q\)-Hermite polynomial
• An extended class of orthogonal polynomials defined by a Sturm-Liouville problem
• Equilibrium positions, shape invariance and Askey–Wilson polynomials
• Exactly Solvable 'Discrete' Quantum Mechanics; Shape Invariance, Heisenberg Solutions, Annihilation-Creation Operators and Coherent States
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Exactly solvable birth and death processes
• Matrices, differential operators, and polynomials
• Quantum versus classical integrability in Calogero$ndash$Moser systems
• Quantum versus classical integrability in Ruijsenaars–Schneider systems
• Equilibria of ‘discrete’ integrable systems and deformation of classical orthogonal polynomials
• Multi-indexed Wilson and Askey–Wilson polynomials
• Finite-dimensional representations of difference operators and the identification of remarkable matrices
• Unified theory of exactly and quasiexactly solvable “discrete” quantum mechanics. I. Formalism
• On the Equilibrium Configuration of the BC-type Ruijsenaars-Schneider System
• Orthogonal polynomials from Hermitian matrices
• The Factorization Method
• Discrete quantum mechanics

This page was built for publication: Perturbations around the zeros of classical orthogonal polynomials