Explicit Green operators for quantum mechanical Hamiltonians
- We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born-Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.
Author details: | Heinz-Jürgen Flad, Gohar Flad-Harutyunyan, Bert-Wolfgang SchulzeGND |
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DOI: | https://doi.org/10.1142/S1793557120501223 |
ISSN: | 1793-5571 |
ISSN: | 1793-7183 |
Title of parent work (English): | Asian-European journal of mathematics : AEJM |
Subtitle (English): | II. edge-type singularities of the helium atom |
Publisher: | World Scientific |
Place of publishing: | Singapore |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/11/01 |
Publication year: | 2020 |
Release date: | 2023/03/27 |
Tag: | Schrodinger equation; Singular analysis; asymptotic properties of eigenfunctions; many-electron systems |
Volume: | 13 |
Issue: | 7 |
Article number: | 2050122 |
Number of pages: | 64 |
Funding institution: | Deutsche Forschungsgemeinschaft DFGGerman Research Foundation (DFG) [HA; 5739/3-1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |