The Schr\"odinger equation with spatial white noise: the average wave function
Probability
2018-01-30 v2 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We prove a representation for the average wave function of the Schr\"odinger equation with a white noise potential in , in terms of the renormalized self-intersection local time of a Brownian motion.
Cite
@article{arxiv.1706.01351,
title = {The Schr\"odinger equation with spatial white noise: the average wave function},
author = {Yu Gu and Tomasz Komorowski and Lenya Ryzhik},
journal= {arXiv preprint arXiv:1706.01351},
year = {2018}
}
Comments
22 pages, minor revisions