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arXiv · 1008.4880

Schrödinger equation with linear potential and hitting times

Gerardo Hernández-del-Valle
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Abstract

In Hernández-del-Valle (2010) the author studies the connection between Schrödinger's equation and first hitting densities of Brownian motion. Although the author is able to find solutions of a Schrödinger 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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Gerardo Hernández-del-Valle. 2010-08-28. Schrödinger equation with linear potential and hitting times. https://arxiv.org/abs/1008.4880

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