Schr\"odinger equation with linear potential and hitting times
Probability
2010-08-31 v1
Abstract
In Hern\'andez-del-Valle (2010) the author studies the connection between Schr\"odinger's equation and first hitting densities of Brownian motion. Although the author is able to find solutions of a Schr\"odinger type pde he fails---except in some special cases---to construct a solution which satisfies the boundary on the space variable at . In this paper we use an approach used in Bluman and Shtelen (1996) to find solutions which satisfy the pde and boundary condition when .
Cite
@article{arxiv.1008.4880,
title = {Schr\"odinger equation with linear potential and hitting times},
author = {Gerardo Hernández-del-Valle},
journal= {arXiv preprint arXiv:1008.4880},
year = {2010}
}