Title




Propagator and Slater sum in onebody potential theory
 
Author




 
Abstract




For a onebody potential V(r) generating eigenfunctions psi(i)(r) and corresponding eigenvalues epsilon(i), the Feynman propagator K(r, r, t) is simply related to the canonical density matrix C(r,r',beta) by beta > it. The diagonal element S(r,r,beta) of C is the socalled Slater sum of statistical mechanics. Differential equations for the Slater sum are first briefly reviewed, a quite general equation being available for a onedimensional potential V(x). This equation can be solved for a sech(2) potential, and some physical properties of interest such as the local density of states are derived by way of illustration. Then, the Coulomb potential Ze(2)/r is next considered, and it is shown that what is essentially the inverse Laplace transform of S(r,beta)/beta can be calculated for an arbitrary number of closed shells. Blinder has earlier determined the Feynman propagator in terms of Whittaker functions and contact is here established with his work. The currently topical case of Fermion vapours which are harmonically confined is then treated, for both two and three dimensions. Finally, in an Appendix, a perturbation series for the Slater sum is briefly summarized, to all orders in the onebody potential V(r). The corresponding kinetic energy is thereby accessible. 
 
Language




English
 
Source (journal)




Physica status solidi: B: basic research.  Berlin
 
Publication




Berlin
:
2003
 
ISSN




03701972
 
Volume/pages




237
:1
(2003)
, p. 265273
 
ISI




000182801800025
 
Full text (Publisher's DOI)




 
