Schrödinger potentials solvable in terms of the confluent Heun functions

DOI10.1134/S0040577916070023zbMath1350.81011MaRDI QIDQ329889

A. M. Ishkhanyan

Publication date: 24 October 2016

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

integrable potentialconfluent Heun equationstationary Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (13)

A conditionally exactly solvable generalization of the inverse square root potential ⋮ Constructions of the soluble potentials for the nonrelativistic quantum system by means of the Heun functions ⋮ Solving eigenproblem by duality transform ⋮ Solutions of the bi-confluent Heun equation in terms of the Hermite functions ⋮ Euler integral symmetries and the asymptotics of the monodromy for the Heun equation ⋮ Schrödinger potentials solvable in terms of the general Heun functions ⋮ Exact solutions of the harmonic oscillator plus non-polynomial interaction ⋮ Four-parameter \(1/r^2\) singular short-range potential with rich bound states and a resonance spectrum ⋮ Exact solutions of the sextic oscillator from the bi-confluent Heun equation ⋮ Scalar field in Reissner-Nordström spacetime: bound state and scattering state (with appendix on eliminating oscillation in partial sum approximation of periodic function) ⋮ Generalized confluent hypergeometric solutions of the Heun confluent equation ⋮ SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS ⋮ γ-rigid version of Bohr Hamiltonian with the modified Davidson potential in the position-dependent mass formalism

Cites Work

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• Potentials of the Heun class
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• New Soluble Energy Band Problem
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics
• On the Vibrations of Polyatomic Molecules
• Solutions for confluent and double-confluent Heun equations
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