Stochastic Shrodinger equations.

[Alexey]

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.

 

[arcnets]

Are you talking about quantum Brownian motion??

 

[Alexey]

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

Yes it is.

 

[arcnets]

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

 

[Alexey]

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.