Open AccessRemarks on Mayer's Reduced Density Matrix Method
Author(s) -
Yukio Mizuno,
Takeo Izuyama
Publication year - 1957
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.18.33
Subject(s) - physics , ground state , density matrix , matrix (chemical analysis) , variation (astronomy) , imperfect , electron density , fermion , statistical physics , electron , quantum mechanics , astrophysics , quantum , chemistry , linguistics , philosophy , chromatography
Mayer has proposed a variation method of finding the two-body reduced density matrix p~ for the ground state of a many fermion system. In this paper it is shown explicitly that his variation method is imperfect and sometimes leads to quite unsatisfactory results. Further, his trial form of p~ for electron gas is translated into that for the 77: electron system of benzene molecule and it is shown that such a trial form is unsatisfactory in several respects. The rigorous analysis of an assembly of mutually interacting particles by means of quantum theory constitutes a very difficult problem ; therefore, we must resort to some approximate methods. One of the most useful approximate methods is the well-known variation method based on the Schrodinger variation principle. In this method an ap· propriate trial form is assumed for the total wave function and the best is sought of all the wave functions of this type. The configuration interaction (CI) procedure in orbital theories is a typical example of this method. It is, however, usually necessary to take into account a very large number of configurations in order to obtain satisfactory results by means of CI procedure. Accordingly, it cannot be said to be a very useful procedure. In order to avoid this difficulty,
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom