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Stochastics Shrodinger equations.

Alexey
in Linear Algebra and Group Theory

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Dear frands!

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.

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