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Explicit Green operators for quantum mechanical Hamiltonians. I. The hydrogen atom

  • We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic structure theory in order to establish accurate and efficient models for numerical simulations. Within our approach, coalescence points of particles are treated as embedded geometric singularities in the configuration space of electrons. Based on a general singular pseudo-differential calculus, we provide a recursive scheme for the calculation of the parametrix and corresponding Green operator of a nonrelativistic Hamiltonian. In our singular calculus, the Green operator encodes all the asymptotic information of the eigenfunctions. Explicit calculations and an asymptotic representation for the Green operator of the hydrogen atom and isoelectronic ions are presented.

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Author:Heinz-Jürgen Flad, Gohar Harutyunyan, Reinhold Schneider, Bert-Wolfgang SchulzeGND
ISSN:0025-2611 (print)
Parent Title (English):Manuscripta mathematica
Place of publication:New York
Document Type:Article
Year of first Publication:2011
Year of Completion:2011
Release Date:2017/03/26
First Page:497
Last Page:519
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert