A note on Schr\'odinger equation with linear potential and hitting times
| Autor: | Hernández-del-Valle, Gerardo |
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| Rok vydání: | 2010 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $x=0$. |
| Databáze: | arXiv |
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