# Stochastic Shrodinger equations.

Dear frends!
Prompt please references to works in which it was considered the Schrodinger equation with stochastic (random) Gaussian delta-correlated potential which
time-dependent and spaces-dependent and with zero average (gaussian delta-correlated noise). I am interesting what average wave function is equal.

U - potential.
<> - simbol of average.

P(F) - density of probability of existence of size F.

Delta-correlated potential which
time-dependent and spaces-dependent:
<U(x,t)U(x,t)>=A*delta(x-x) *delta(t-t)
delta - delta-function of Dirack.
A - const.

Zero average:
<U(x,t)>=0

Gaussian potential (existence of probability is distributed on Gauss law):
P(U)=C*exp(U^2/delU^2)

C - normalizing constant.
delU - root-mean-square fluctuation of U.

Are you talking about quantum Brownian motion??

Originally posted by arcnets
Are you talking about quantum Brownian motion??

Yes it is.

Google gives some hits on "quantum Brownian motion", maybe there's what you're looking for.

Originally posted by arcnets
Google gives some hits on "quantum Brownian motion", maybe there's what you're looking for.

Thanck you! I find any-thing.