Title




Nonrelativistic and relativistic electron liquids confined by a linear potential
 
Author




 
Abstract




The theory of fermion particle densities in a confining linear scalar potential energy V(x) = g\x\ is considered in both nonrelativistic and relativistic quantum mechanics. In the former case., some analytic progress proves possible for weak potentials (small g), by consideration of the canonical density matrix, having the Slater sum as its diagonal element. For larger values of g, some numerical results for the fermion density rho(x) are presented, from essentially the properties of Airy functions. The influence of a nonzero value of the Compton wavelength lambda = h/m(o)c, with m(o) the fermion rest mass, is then considered using relativistic ThomasFermi theory. For future work, the treatment of Hiller from the Dirac equation should prove amenable to numerical computation of the relativistic fermion density rho(lambda)(x), for comparison with the ThomasFermi results presented here. The possibility of relativistic and nonrelativistic densities being related by a difference equation with an interval determined by lambda is briefly referred to. 
 
Language




English
 
Source (journal)




Physics and chemistry of liquids.  London
 
Publication




London
:
2005
 
ISSN




00319104
 
DOI




10.1080/00319100500040963
 
Volume/pages




43
:3
(2005)
, p. 225237
 
ISI




000229744400001
 
Full text (Publisher's DOI)




 
