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Upper and lower bounds in second‐order perturbation theory and the unsÖld approximation
Author(s) -
Lindner Peter,
Löwdin PerOlov
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560020717
Subject(s) - upper and lower bounds , perturbation (astronomy) , mathematics , perturbation theory (quantum mechanics) , operator (biology) , order (exchange) , mathematical analysis , mathematical physics , quantum mechanics , physics , chemistry , biochemistry , finance , repressor , transcription factor , economics , gene
Abstract Upper and lower bounds for the second‐order energy in the SchrÖdinger perturbation theory are studied by means of operator inequalities and inner projections. It is shown that the variation problems associated with Hylleraas's upper bound and Hirschfelder‐Prager's lower bound over a linear manifold have simple explicit solutions. The approach is tested numerically on some selected examples with good results.