Exact solutions of a Schrödinger equation based on the Lambert function

DOI10.1016/j.physleta.2004.11.012zbMath1123.34301OpenAlexW2007320875MaRDI QIDQ2463205

Brian Wesley Williams

Publication date: 5 December 2007

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

Full work available at URL: https://doi.org/10.1016/j.physleta.2004.11.012

zbMATH Keywords

supersymmetricLambert functionexactly solvableconfluent Natanzon

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Schrödinger operator, Schrödinger equation (35J10) Elementary classical functions (33B99)

Related Items (3)

The third five-parametric hypergeometric quantum-mechanical potential ⋮ Schrödinger potentials solvable in terms of the confluent Heun functions ⋮ Four five-parametric and five four-parametric independent confluent Heun potentials for the stationary Klein-Gordon equation

Uses Software

• Mathematica

Cites Work

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• Exact solutions of the Schrödinger equation for the deformed hyperbolic potential well and the deformed four-parameter exponential type potential
• General properties of potentials for which the Schrödinger equation can be solved by means of hypergeometric functions
• On the Lambert \(w\) function
• ``Implicit potentials associated with Jacobi polynomials: Some novel aspects
• A class of exactly solvable potentials related to the Jacobi polynomials
• 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
• Solvable potentials associated with su(1,1) algebras: a systematic study
• A class of solvable potentials

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