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arXiv · 1009.0730

A note on Schr\"odinger equation with linear potential and hitting times

Gerardo Hernández-del-Valle
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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 $\lambda$, 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 $x=0$.

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Gerardo Hernández-del-Valle. 2010-09-03. A note on Schr\"odinger equation with linear potential and hitting times. https://arxiv.org/abs/1009.0730

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