Rigorous lower and upper bounds on the lowest three eigenvalues of the two-electron atomic Hamiltonian are obtained for the symmetry sectors 1 S, 3 S, 1 P, 3 P and the sector 3 P o with unnatural parity. The bounds result from three-dimensional projection operators and are given as explicit expressions that depend on the nuclear charge Z as parameter. They are designed for application within further analysis, and we exemplify this by demonstrating monotonicity properties of excitation energies.
Description
SpringerLink - Journal of Mathematical Chemistry, Volume 49, Number 10
%0 Journal Article
%1 springerlink:10.1007/s10910-011-9879-3
%A Hogreve, H.
%D 2011
%I Springer Netherlands
%J Journal of Mathematical Chemistry
%K analysis energy inequality mathematics mechanics operator physics quantum
%N 10
%P 2177-2189
%R 10.1007/s10910-011-9879-3
%T Rigorous energy bounds for two-electron systems
%U http://dx.doi.org/10.1007/s10910-011-9879-3
%V 49
%X Rigorous lower and upper bounds on the lowest three eigenvalues of the two-electron atomic Hamiltonian are obtained for the symmetry sectors 1 S, 3 S, 1 P, 3 P and the sector 3 P o with unnatural parity. The bounds result from three-dimensional projection operators and are given as explicit expressions that depend on the nuclear charge Z as parameter. They are designed for application within further analysis, and we exemplify this by demonstrating monotonicity properties of excitation energies.
@article{springerlink:10.1007/s10910-011-9879-3,
abstract = {Rigorous lower and upper bounds on the lowest three eigenvalues of the two-electron atomic Hamiltonian are obtained for the symmetry sectors 1 S, 3 S, 1 P, 3 P and the sector 3 P o with unnatural parity. The bounds result from three-dimensional projection operators and are given as explicit expressions that depend on the nuclear charge Z as parameter. They are designed for application within further analysis, and we exemplify this by demonstrating monotonicity properties of excitation energies.},
added-at = {2011-10-22T21:50:40.000+0200},
affiliation = {IFISR–International Foundation for Independent Scientific Research, 1133 Broadway Suite 706, New York, NY 10010, USA},
author = {Hogreve, H.},
biburl = {https://www.bibsonomy.org/bibtex/2fa8ac1a9abfdf4bfd7ff265e02ab136a/drmatusek},
description = {SpringerLink - Journal of Mathematical Chemistry, Volume 49, Number 10},
doi = {10.1007/s10910-011-9879-3},
interhash = {fb4782151975f9eda3d56b9262f59847},
intrahash = {fa8ac1a9abfdf4bfd7ff265e02ab136a},
issn = {0259-9791},
issue = {10},
journal = {Journal of Mathematical Chemistry},
keyword = {Chemistry and Materials Science},
keywords = {analysis energy inequality mathematics mechanics operator physics quantum},
month = {November},
number = 10,
pages = {2177-2189},
publisher = {Springer Netherlands},
timestamp = {2012-11-05T03:29:47.000+0100},
title = {Rigorous energy bounds for two-electron systems},
url = {http://dx.doi.org/10.1007/s10910-011-9879-3},
volume = 49,
year = 2011
}