Schrodinger equations are equivalent to pairs of mutually time-reverse
d non-linear diffusion equations. Here the associated diffusion proces
ses with singular drift are constructed under assumptions adopted from
the theory of Schrodinger operators, expressed in terms of a local sp
ace-time Sobolev space. By means of Nagasawa's multiplicative function
al N(s)t, a Radon-Nikodym derivative on the space of continuous paths,
a transformed process is obtained from Wiener measure. Its singular d
rift is identified by Maruyama's drift transformation. For this a vers
ion of Ito's formula for continuous space-time functions with first an
d second order derivatives in the sense of distributions satisfying lo
cal integrability conditions has to be derived. The equivalence is sho
wn between weak solutions of a diffusion equation with singular creati
on and killing term and the solutions of a Feynman-Kac integral equati
on with a locally integrable potential function.