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 |
|---|---|
| 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 |
