%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 }