Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 15, Issue 8, Pages 1169-1180Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202505000698
Keywords
nonlinear Schrodinger equation; quantum semiconductor modeling; semiclassical limit; time-dependent density functional theory
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The Schrodinger-Poisson-X alpha 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 Schrodinger equations. We obtain existence and uniqueness of the Cauchy problem in d = I using semigroup theory. Furthermore, we discuss the semiclassical limit.
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