THE IVP FOR THE SCHRÖDINGER–POISSON-Xα EQUATION IN ONE DIMENSION
2005 ◽
Vol 15
(08)
◽
pp. 1169-1180
◽
Keyword(s):
The Schrödinger–Poisson-Xα equation is an effective one-particle approximation of a many-electron quantum system. In space dimension d<3, existence analysis for this equation is not contained in standard results for nonlinear Schrödinger equations. We obtain existence and uniqueness of the Cauchy problem in d = 1 using semigroup theory. Furthermore, we discuss the semiclassical limit.
2012 ◽
Vol 09
(01)
◽
pp. 177-193
◽
2002 ◽
Vol 2
(3)
◽
pp. 131-139
◽
2015 ◽
Vol 39
(11)
◽
pp. 3116-3135
◽
1978 ◽
Vol 69
(2)
◽
pp. 289-289
◽
2020 ◽
Vol 60
(4)
◽
pp. 663-672