Explicit Green operators for quantum mechanical Hamiltonians
- 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.
Author details: | Heinz-Jürgen Flad, Gohar Harutyunyan, Reinhold Schneider, Bert-Wolfgang SchulzeGND |
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DOI: | https://doi.org/10.1007/s00229-011-0429-x |
ISSN: | 0025-2611 |
Title of parent work (English): | Manuscripta mathematica |
Subtitle (German): | I. The hydrogen atom |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Year of first publication: | 2011 |
Publication year: | 2011 |
Release date: | 2017/03/26 |
Volume: | 135 |
Issue: | 3-4 |
Number of pages: | 23 |
First page: | 497 |
Last Page: | 519 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |