  In Hern\'andez-del-Valle (2010) the author studies the connection between
Schr\"odinger's equation and first hitting densities of Brownian motion.
Although the author is able to find solutions of a Schr\"odinger 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 $t=0$.
