Alternative approach to the solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem

DOI10.1002/andp.201100330zbMath1254.81039arXiv1111.1661OpenAlexW3101622583MaRDI QIDQ2915753

Radosław Szmytkowski

Publication date: 18 September 2012

Published in: Annalen der Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.1661

zbMATH Keywords

integral equationsGegenbauer polynomialsLegendre functionsmomentum representationCoulomb problem

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 of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (5)

Wave functions of the Hydrogen atom in the momentum representation ⋮ Dynamics of atoms in strong laser fields. I: A quasi analytical model in momentum space based on a Sturmian expansion of the interacting nonlocal Coulomb potential ⋮ Heisenberg-like uncertainty measures for D-dimensional hydrogenic systems at large D ⋮ On a generalization of the generating function for Gegenbauer polynomials ⋮ Rydberg multidimensional states: Rényi and Shannon entropies in momentum space

Cites Work

• Solution of Coulomb system in momentum space
• Die Funksche Integralgleichung der Kugelflächenfunktionen und ihre Übertragung auf die Überkugel
• Multipole expansions and Fock symmetry of the hydrogen atom
• Wave equations in momentum space

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