Darboux transformation and nonclassical orthogonal polynomials

DOI10.1007/BF00560101zbMath0944.34070MaRDI QIDQ1968932

I. N. Ovcharov, Boris F. Samsonov

Publication date: 11 September 2000

Published in: Russian Physics Journal (Search for Journal in Brave)

zbMATH Keywords

Schrödinger equationDarboux transformationharmonic oscillator potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Special integral transforms (Legendre, Hilbert, etc.) (44A15) 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) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (3)

DEK-type orthogonal polynomials and a modification of the Christoffel formula ⋮ Conditionally exactly solvable potentials and exceptional orthogonal polynomials ⋮ The factorization method for the Askey-Wilson polynomials

Cites Work

• Unnamed Item
• Series in Faber polynomials and several generalizations
• A correction to the paper ``Hypergeometric functions and toric varieties
• The Darboux transformation and solvable double-well potential models for Schrödinger equations
• Factorization method and new potentials with the oscillator spectrum
• A class of exactly solvable potentials related to the Jacobi polynomials

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