Title 



The determination of the Dirac density matrix of the ddimensional harmonic oscillator for an arbitrary number of closed shells
 
Author 



 
Abstract 



In 1959, March and Young (Nucl. Phys. 12 237) rewrote the equation of motion for the Dirac density matrix gamma(x, x(0)) in terms of sum and difference variables. Here, gamma((r) over right arrow, (r) over right arrow (0)) for the ddimensional isotropic harmonic oscillator for an arbitrary number of closed shells is shown to satisfy, using the variables \(r) over bar + (r) over bar (0)\/2 and \(r) over right arrow  (r) over right arrow (0)\/2, a generalized partial differential equation embracing the MarchYoung equation for d = 1. As applications, we take in turn the cases d = 1, 2, 3 and 4, and obtain both the density matrix gamma((r) over right arrow,(r) over right arrow (0)) and the diagonal density rho(r) = gamma((r) over right arrow, (r) over right arrow (0))\((r) over right arrow0=(r) over right arrow), this diagonal element already being known to satisfy a thirdorder linear homogeneous differential equation for 1 through 3. Some comments are finally made on the ddimensional kinetic energy density, which is important for firstprinciples density functional theory in allowing one to bypass oneparticle Schrodinger equations (the socalled SlaterKohnSham equations).   
Language 



English
 
Source (journal) 



Journal of physics: A: mathematical and general.  London, 1968  2006  
Publication 



London : 2002
 
ISSN 



03054470
 
Volume/pages 



35:24(2002), p. 49854997
 
ISI 



000176858400004
 
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