Linear Schrodinger evolution equations with moving Coulomb singularities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Okazawa, Noboru¹  Yoshii, Kentarou¹ 

[1] Tokyo Univ Sci, Tokyo 162, Japan

关键词: Schrodinger equation;    Moving Coulomb singularities;    Potentials with singularity at infinity;    Existence and uniqueness of C-1 solutions;    Linear evolution equations;    Hyperbolic type;   

DOI  :  10.1016/j.jde.2013.01.017

来源: Elsevier

【 摘 要 】

The Cauchy problem for Schrodinger evolution equations with a finite number of moving Coulomb singularities is investigated. The case of a single singularity has been studied by several authors (see, e.g., Baudouin et al. (2005) [1] and Okazawa et al. (2010) [19]). However, it seems to be no previous work on plural singularities. We shall show that the problem has a unique (classical) solution by using a time-dependent linear transformation of the unknown function which locally freezes the motion of the whole singularities under the simplest collisionless condition. In fact, a new existence and uniqueness theorem is available for the transformed problem. Such an abstract framework is established from the viewpoint of linear evolution equations of hyperbolic type in a Hilbert space as an innovative modification of those in Okazawa (1998) [17] and Okazawa and Yoshii (2011) [20]. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free