Journal of Applied Mathematics
Volume 2012 (2012), Article ID 387823, 15 pages
http://dx.doi.org/10.1155/2012/387823
Research Article

A Nonlinear Schrödinger Model for Many-Particle Quantum Systems

Qiang Zhang1,2 and Tian Ma2

1College of Computer Science, Civil Aviation Flight University of China, Guanghan 618307, China
2Department of Mathematics, Sichuan University, Chengdu 610064, China

Received 1 June 2012; Revised 10 August 2012; Accepted 5 September 2012

Academic Editor: K. S. Govinder

Copyright © 2012 Qiang Zhang and Tian Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Considering both effects of the s-wave scattering and the atom-atom interaction rather than only the effect of the s-wave scattering, we establish a nonlinear Schrödinger model for many-particle quantum systems and we prove the global existence of a solution to the model and obtain the expression of the solution. Furthermore, we show that the Hamilton energy and the total particle number both are conservative quantities.