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The density matrix in the two‐particle function method
Author(s) -
Mestechkin M. M.
Publication year - 1967
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.560010517
Subject(s) - eigenvalues and eigenvectors , degeneracy (biology) , matrix (chemical analysis) , singlet state , function (biology) , density matrix , kernel (algebra) , spectrum (functional analysis) , mathematics , physics , mathematical physics , pure mathematics , mathematical analysis , combinatorics , quantum mechanics , chemistry , excited state , bioinformatics , chromatography , evolutionary biology , quantum , biology
The first‐ and second‐order density matrices D ( N ) and D 2 ( N )for the function g ( n ) = A N [ g (1, 2) … g ( N − 1, N )] are expressed by the g function itself and its density matrix D . In a singlet state the generating functions for spatial parts of these matrices are simply connected with there solvent of the Fredholm equation in which the spatial part of D is a kernel. Some special cases of g (1, 2) are considered. It isestablished that the number of large eigenvalues of D 2 ( N )does not exceed that of different eigenvalues of D . Thus the degeneracy in the spectrum of D causes the appearance of such large eigenvalues.