TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Flad-Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Explicit Green operators for quantum mechanical Hamiltonians
BT  - II. edge-type singularities of the helium atom
JF  - Asian-European journal of mathematics : AEJM
N2  - 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.
KW  - Singular analysis
KW  - Schrodinger equation
KW  - many-electron systems
KW  - asymptotic properties of eigenfunctions
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557120501223
SN  - 1793-5571
SN  - 1793-7183
VL  - 13
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Flad-Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Ellipticity of the quantum mechanical Hamiltonians
BT  - corner singularity of the helium atom
JF  - Journal of pseudo-differential operators and applications
N2  - In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0201-4
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 3
SP  - 451
EP  - 467
PB  - Springer
CY  - Basel
ER  -