The IVP for the Schrodinger-Poisson-Xα equation in one dimension

被引：14
作者：
Stimming, HP [1 ]
机构：
[1] Univ Vienna, Fak Math, Wolfgang Pauli Inst, A-1090 Vienna, Austria
来源：
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2005年 / 15卷 / 08期
关键词：
nonlinear Schrodinger equation; quantum semiconductor modeling; semiclassical limit; time-dependent density functional theory;
D O I：
10.1142/S0218202505000698
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：1169 / 1180
页数：12
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