Schrödinger equation with linear potential and hitting times

2010/08/28 by Gerardo Hernández-del-Valle, Hernández-del-Valle, Gerardo
Mathematics · #45D05 #45G10 #45K05 #45Q05 #60J60 #FOS: Mathematics #Primary: 60J65 #Probability (math.PR) #Secondary: 45G15 #math.PR #msc:45D05 #msc:45G10 #msc:45G15 #msc:45K05 #msc:45Q05 #msc:60J60 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1008.4880

arxiv created 2010/08/28 · arxiv updated 2010/08/31

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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