Remarks about the wave-function representability of the first-order reduced density matrices

1986 ◽  
Vol 30 (S20) ◽  
pp. 769-771 ◽  
Author(s):  
Per-Olov L�wdin
Keyword(s):  
Wave Function ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
First Order ◽  
Reduced Density

Über die Symmetrie-Eigenschaften der reduzierten Dichtematrizen und der natürlichen Spin-Orbitale und Spin-Geminale (der natürlichen Ein- und Zwei-Elektronen-Funktionen)

1963 ◽  
Vol 18 (10) ◽  
pp. 1058-1064 ◽  
Author(s):  
Werner Kutzelnigg
Keyword(s):  
Wave Function ◽  
Density Matrix ◽  
Symmetry Group ◽  
Total Wave Function ◽  
Irreducible Representations ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Total Wave ◽  
Definition Of ◽  
Reduced Density

The density operator (density matrix) of a quantum mechanical system can be decomposed into operators which transform as irreducible representations of the symmetry group in coordinate and spin space. Each of these components has a physical meaning connected with the expectation values of certain operators. The reduced density matrices can be decomposed in a completely analogous way.The symmetry properties of the total wave function give rise to degeneracies of the eigenvalues of the reduced density matrices. These degeneracies can be removed by requiring that the natural spin orbitals (NSO, defined as the eigenfunctions of the first order density matrix), as well as the natural spin geminais (NSG, the eigenfunctions of the second order density matrix) and their spinless counterparts transform as irreducible representations of the symmetry group and are eigenfunctions of S2 and Sz.In many important cases this requirement is compatible with the original definition of the NSO, the NSG etc. e. g., when there is no spatial degeneracy of the total wave function and when the Z-component of the total spin vanishes. When these conditions are not fulfilled an alternative definition of the NSO and the NSG is proposed.

Reduced Density Matrices

2000 ◽  
Author(s):  
A. John Coleman ◽  
Vyacheslav I. Yukalov
Keyword(s):  
Density Matrices ◽  
Reduced Density Matrices ◽  
Reduced Density
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