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Stochastic equations.

  1. Jul 14, 2003 #1
    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.
     
  2. jcsd
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