Unified treatment of the Coulomb and harmonic oscillator potentials in D dimensions

DOI10.1063/1.532595zbMath0935.81016arXivquant-ph/9802012OpenAlexW2002065090MaRDI QIDQ4701520

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Publication date: 21 November 1999

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

Full work available at URL: https://arxiv.org/abs/quant-ph/9802012

zbMATH Keywords

Green's operator\(SU(1,1)\) algebraHilbert space basisgeneralized Coulomb potentialgeneralized Coulomb-Sturmian basisharmonic oscillator potentials

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

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Cites Work

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• Two singular potentials: The space-splitting effect
• The generalized Coulomb problem: an exactly solvable model
• Green’s matrix from Jacobi-matrix Hamiltonian
• An integrated approach to ladder and shift operators for the Morse oscillator, radial Coulomb and radial oscillator potentials
• Solvable potentials associated with su(1,1) algebras: a systematic study
• Comment on 'Penetrability of a one-dimensional Coulomb potential' by M. Moshinsky
• The functional–analytic versus the functional–integral approach to quantum Hamiltonians: The one-dimensional hydrogen atoma)

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