On the Schr\"odinger equation with singular potentials
Analysis of PDEs
2013-07-29 v1
Abstract
We study the Cauchy problem for the non-linear Schr\"odinger equation with singular potentials. For point-mass potential and nonperiodic case, we prove existence and asymptotic stability of global solutions in weak-L^{p} spaces. Specific interest is give to the point-like and impurity and for two -interactions in one dimension. We also consider the periodic case which is analyzed in a functional space based on Fourier transform and local-in-time well-posedness is proved.
Cite
@article{arxiv.1307.6895,
title = {On the Schr\"odinger equation with singular potentials},
author = {Jaime Angulo Pava and Lucas C. F. Ferreira},
journal= {arXiv preprint arXiv:1307.6895},
year = {2013}
}