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.

引用

页码：1169 / 1180

页数：12

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