Premium
Path integral formulation for many‐electron system
Author(s) -
Kawabe H.,
Nagao H.,
Nishikawa K.
Publication year - 1996
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/(sici)1097-461x(1996)59:6<457::aid-qua3>3.0.co;2-x
Subject(s) - path integral formulation , relation between schrödinger's equation and the path integral formulation of quantum mechanics , feynman diagram , electron , partition function (quantum field theory) , gaussian , closure (psychology) , quantum , quantum mechanics , linear combination of atomic orbitals , path (computing) , amplitude , functional integration , integral equation , mathematics , statistical physics , physics , atomic orbital , mathematical analysis , computer science , economics , market economy , programming language
The Feynman path integral method is applied to the many‐electron problem of quantum chemistry. We begin with constructing new closure relations in terms of the linear combination of atomic orbital (LCAO) coefficients and investigate the transition amplitude and the partition function of the system in question; then a “classical path of electrons,” which is described by the time‐dependent Hartree‐Fock‐Roothaan equation, is obtained by minimizing the action integral of the system with respect to the “electron coordinate.” The next order approximation is obtained by evaluating the deviation from this classical path, which is approximately written by a Gaussian integral. The result is expected to be the random‐phase approximation. © 1996 John Wiley & Sons, Inc.