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• W2014209007 endingPage "1489" @default.
• W2014209007 startingPage "1474" @default.
• W2014209007 abstract "In order to calculate the average value of a physical quantity containing also many-particle interactions in a system of $N$ antisymmetric particles, a set of generalized density matrices are defined. In order to permit the investigation of the same physical situation in two complementary spaces, the Hermitean density matrix of order $k$ has two sets of indices of each $k$ variables, and it is further antisymmetric in each set of these indices.Every normalizable antisymmetric wave function may be expanded in a series of determinants of order $N$ over all ordered configurations formed from a basic complete set of one-particle functions ${ensuremath{psi}}_{k}$, which gives a representation of the wave function and its density matrices also in the discrete $k$-space. The coefficients in an expansion of an eigenfunction to a particular operator may be determined by the variation principle, leading to the ordinary secular equation of the method of configurational interaction. It is shown that the first-order density matrix may be brought to diagonal form, which defines the natural spin-orbitals associated with the system. The situation is then partly characterized by the corresponding occupation numbers, which are shown to lie between 0 and 1 and to assume the value 1, only if the corresponding spin-orbital occurs in all configurations necessary for describing the situation. If the system has exactly $N$ spin-orbitals which are fully occupied, the total wave function may be reduced to a single Slater determinant. However, due to the mutual interaction between the particles, this limiting case is never physically realized, but the introduction of natural spin-orbitals leads then instead to a configurational expansion of most rapid convergence.In case the basic set is of finite order $M$, the best choice of this set is determined by a form of extended Hartree-Fock equations. It is shown that, in this case, the natural spin-orbitals approximately fulfill some equations previously proposed by Slater." @default.
• W2014209007 created "2016-06-24" @default.
• W2014209007 creator A5012651484 @default.
• W2014209007 date "1955-03-15" @default.
• W2014209007 modified "2023-10-18" @default.
• W2014209007 title "Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction" @default.
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• W2014209007 doi "https://doi.org/10.1103/physrev.97.1474" @default.
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