``Implicit potentials associated with Jacobi polynomials: Some novel aspects

DOI10.1016/0375-9601(95)00059-CzbMath1020.81939MaRDI QIDQ1965473

Géza Lévai, Jennifer L. Rutherford, Brian Wesley Williams

Publication date: 8 February 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) (2)-body potential quantum scattering theory (81U05) Applications of hypergeometric functions (33C90)

Related Items (7)

Accidental crossing of energy eigenvalues in \(\mathcal{P}T\)-symmetric Natanzon-class potentials ⋮ Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems ⋮ \({\mathcal {PT}}\) symmetry in Natanzon-class potentials ⋮ Exact solutions of a Schrödinger equation based on the Lambert function ⋮ Conditionally exactly solvable potentials and supersymmetric transformations ⋮ An exactly solvable Schrödinger equation with finite positive position-dependent effective mass ⋮ An extended scenario for the Schrödinger equation

Cites Work

• Dynamical breaking of supersymmetry
• General properties of potentials for which the Schrödinger equation can be solved by means of hypergeometric functions
• Single-variable realisation of the SU(1,1) spectrum generating algebra and discrete eigenvalue spectra of a class of potentials
• A class of exactly solvable potentials related to the Jacobi polynomials
• Phase-equivalent potentials from supersymmetry
• A second class of solvable potentials related to the Jacobi polynomials
• A search for shape-invariant solvable potentials
• The generalized Coulomb problem: an exactly solvable model
• Analysis of inverse-square potentials using supersymmetric quantum mechanics
• A class of solvable potentials

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