The d-dimensional softcore Coulomb potential and the generalized confluent Heun equation

DOI10.1063/1.5035357zbMath1400.81093arXiv1810.06539OpenAlexW3098169261MaRDI QIDQ4556623

Nasser Saad, Kyle R. Bryenton, Richard L. Hall

Publication date: 16 November 2018

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

Full work available at URL: https://arxiv.org/abs/1810.06539

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Special quantum systems, such as solvable systems (81Q80)

Uses Software

• DLMF

Cites Work

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• Location of the zeros of polynomials satisfying three-term recurrence relations. III. Positive coefficients case
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• Spectral characteristics for a spherically confined −a/r+br²potential
• Physical applications of second-order linear differential equations that admit polynomial solutions
• The interaction V(r)=-Ze²/(r+ beta ) and the confluent Heun equation
• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• The Schrodinger equation for the interaction potential x²+λx²/(1+gx²) and the first Heun confluent equation
• Solutions for the general, confluent and biconfluent Heun equations and their connection with Abel equations
• Soft-core Coulomb potentials and Heun’s differential equation
• Confluent Heun functions and separation of variables in spheroidal coordinates
• Quasi-exactly solvable systems and orthogonal polynomials
• Sextic anharmonic oscillators and orthogonal polynomials
• Solutions for confluent and double-confluent Heun equations
• An exclusion theorem for tri-diagonal matrices
• Eigenvalues of complex tridiagonal matrices

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