Analysis of the Statistical Density Matrix
Abstract
A generalized expression for the statistical field has been obtained which includes the ThomasFermi and ThomasFermiDirac fields as special cases. The behavior of the energy, charge density, boundary density, and electron groups has been investigated for various fields. Fields with exchange are obtained with behave like the ThomasFermi field at the boundary. A singularity in the ThomasFermiDirac density matrix has been found which leads to an oscillation in the sign of the charge in high angular momentum states. This singularity is related to the necessity for terminating the ThomasFermiDirac distribution at a finite boundary. Comparison of the Fourier components and wave functions calculated from statistical density matrices for Cu^{+} with the corresponding HartreeFock values has revealed that it would not be useful to use the statistical density matrix as a starting point for a HartreeFock calculation.
 Publication:

Physical Review
 Pub Date:
 November 1961
 DOI:
 10.1103/PhysRev.124.785
 Bibcode:
 1961PhRv..124..785K