Premium
Variational marginal amplitudes
Author(s) -
Hunter Geoffrey,
Tai Chin Chiu
Publication year - 1982
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.560210608
Subject(s) - wave function , mathematics , amplitude , helium atom , subspace topology , domain (mathematical analysis) , mathematical analysis , variational principle , schrödinger equation , wave equation , function (biology) , space (punctuation) , physics , quantum mechanics , helium , linguistics , philosophy , evolutionary biology , biology
The theory by which a wave function may be factorized into conditional and marginal amplitudes is extended to the domain of approximate wave functions. The approximate conditional and marginal factors are well defined, and the marginal factor satisfies a variation principle that is equivalent to a reduced Schrödinger equation having the same form as that derived in the case of exact wave functions. Of the two ways of calculating the effective potential in the reduced Schrödinger equation (which are equivalent in the case of exact wave functions), the integral method is demonstrated to be intrinsically more accurate than the differential method. The variation principle for the marginal amplitude leads to a technique for improving approximate wave functions within a subspace of the whole configuration space. These concepts are illustrated by calculations on the ground state of the helium atom.