Schrödinger equation with linear potential and hitting times

Details Schrödinger equation with linear potential and hitting times Schrödinger equation with linear potential and hitting times

2010-08-28

arxiv.org/abs/1008.4880v1

Mathematics

Probability

Scientific paper

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

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