Confluent Heun functions and separation of variables in spheroidal coordinates

DOI10.1063/1.3613651zbMath1317.35019OpenAlexW2045226904MaRDI QIDQ5266105

Rufus Boyack, John Lekner

Publication date: 29 July 2015

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

Full work available at URL: https://doi.org/10.1063/1.3613651

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Schrödinger operator, Schrödinger equation (35J10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Lamé, Mathieu, and spheroidal wave functions (33E10)

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The d-dimensional softcore Coulomb potential and the generalized confluent Heun equation ⋮ Theoretical solution for the axial vibration of functionally graded double-lap adhesive joints

Uses Software

• Maple

Cites Work

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• The interaction V(r)=-Ze²/(r+ beta ) and the confluent Heun equation
• A limit of the confluent Heun equation and the Schrödinger equation for an inverted potential and for an electric dipole
• The Schrodinger equation for the interaction potential x²+λx²/(1+gx²) and the first Heun confluent equation
• Theory and computation of spheroidal wavefunctions
• Soft-core Coulomb potentials and Heun’s differential equation

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