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Upper and lower bounds and the generalized variation‐perturbation approach of many‐electron theory
Author(s) -
Goscinski Osvaldo,
Sinanoǧlu Oktay
Publication year - 1968
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.560020309
Subject(s) - upper and lower bounds , bracketing (phenomenology) , perturbation theory (quantum mechanics) , mathematics , perturbation (astronomy) , electron , statistical physics , physics , quantum mechanics , mathematical analysis , philosophy , epistemology
The theory of upper and lower bounds is used in conjunction with the “varied‐portions approach” ( VPA ) of the “many‐electron theory of atoms and molecules” ( MET ). Upper and lower bounds equations are derived. It is recognized that if a very natural portion of the full variational expression is made stationary, according to ( VPA ), a for of Löwdin's lower bound wave equation results. By using the bracketing theorem it is also possible to give lower bounds to the quantities arising from the ( VPA ) of ( MET ). This will be useful to study in the future the ( MET ) pair correlations and to supplement the computational methods currently available with lower bound estimates as well.