A note on Schr\"odinger equation with linear potential and hitting times
Probability
2010-09-06 v1 Mathematical Physics
math.MP
Abstract
In this note we derive a solution to the Schr\"odinger-type backward equation which satisfies a necessary boundary condition used in hitting-time problems [as described in Hern\'andez-del-Valle (2010a)]. We do so by using an idea introduced by Bluman and Shtelen (1996) which is worked out in Hern\'andez-del-Valle (2010b). This example is interesting since it is independent of the parameter , namely: \kappa(s,x)=\frac{x}{\sqrt{2\pi s}}\exp{-\frac{(x+\int_0^sf'(u))^2}{2s}}. and suggest a procedure to generating more vanishing solutions and .
Cite
@article{arxiv.1009.0730,
title = {A note on Schr\"odinger equation with linear potential and hitting times},
author = {Gerardo Hernández-del-Valle},
journal= {arXiv preprint arXiv:1009.0730},
year = {2010}
}