Schrodinger equation with stochastic potential.

[Alexey]

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.

[Tom Mattson]

Hi,

 

I'm not sure of what you're talking about, but if you could type out the expression for the potential I might be able to help. There are math symbols in the Smilies menu to the left when you reply. Click on "Get More".

[Alexey]

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*:lcdelta:(x-x`) *:lcdelta:(t-t`)

:lcdelta: - 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.

[Alexey]

Look please my answer at your question.

[Tom Mattson]

Alexey said in post #4 :

Look please my answer at your question.

 

Sorry, I haven't been around here in a while. Besides, I saw that someone helped you with this at Physics Forums. I don't know much about this myself.

 

Are you still stuck?