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
 
DOI




10.1088/03054470/35/24/302
 
Volume/pages




35
:24
(2002)
, p. 49854997
 
ISI




000176858400004
 
Full text (Publisher's DOI)




 
Full text (publisher's version  intranet only)




 
