A class of exactly solvable potentials related to the Jacobi polynomials

DOI10.1088/0305-4470/24/1/022zbMath0728.34092OpenAlexW1982484947MaRDI QIDQ3351763

Géza Lévai

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1088/0305-4470/24/1/022

zbMATH Keywords

eigenvaluesnormal formeigenfunctionsJacobi polynomialsone-dimensional Schrödinger equationsupersymmetric potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) 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) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (13)

\({\mathcal {PT}}\) symmetry in Natanzon-class potentials ⋮ ``Implicit potentials associated with Jacobi polynomials: Some novel aspects ⋮ Darboux transformation and exactly solvable potentials with quasi-equidistant spectrum ⋮ Some properties of higher-order Darboux transformations ⋮ Darboux transformation and nonclassical orthogonal polynomials ⋮ Solvable models of an open well and a bottomless barrier: one-dimensional exponential potentials ⋮ Exact solutions of a Schrödinger equation based on the Lambert function ⋮ Shape invariant Natanzon potential hierarchy and its twin: a novel approach ⋮ Unified treatment of the Coulomb and harmonic oscillator potentials in D dimensions ⋮ Conditionally exactly solvable potentials and supersymmetric transformations ⋮ An exactly solvable Schrödinger equation with finite positive position-dependent effective mass ⋮ SUPERSYMMETRIC APPROACH TO QUASINORMAL MODES ⋮ An extended scenario for the Schrödinger equation

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