English

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 x=0x=0. In this paper we use an approach used in Bluman and Shtelen (1996) to find solutions which satisfy the pde and boundary condition when t=0t=0.

Keywords

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}
}
R2 v1 2026-06-21T16:06:20.110Z