TY  - JOUR
A1  - Flad, Heinz-Jürgen
A1  - Harutyunyan, Gohar
A1  - Schneider, Reinhold
A1  - Schulze, Bert-Wolfgang
T1  - Explicit Green operators for quantum mechanical Hamiltonians
BT  - I. The hydrogen atom
JF  - Manuscripta mathematica
N2  - 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.
Y1  - 2011
U6  - https://doi.org/10.1007/s00229-011-0429-x
SN  - 0025-2611
VL  - 135
IS  - 3-4
SP  - 497
EP  - 519
PB  - Springer
CY  - New York
ER  -