Stochastic Shrodinger equations.

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Discussion Overview

The discussion revolves around the Schrödinger equation with a stochastic Gaussian delta-correlated potential that is both time-dependent and space-dependent, specifically focusing on its implications and the average wave function. Participants explore the nature of the potential and its statistical properties.

Discussion Character

  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant requests references to works discussing the Schrödinger equation with a stochastic Gaussian delta-correlated potential, specifying conditions such as zero average and the nature of the potential.
  • Another participant suggests that the topic may relate to quantum Brownian motion.
  • The original poster confirms that their inquiry is indeed about quantum Brownian motion.
  • A suggestion is made to use Google for further information on quantum Brownian motion, which may contain relevant references.
  • The original poster expresses gratitude but indicates difficulty in finding relevant materials.

Areas of Agreement / Disagreement

Participants appear to agree on the connection between the discussed stochastic potential and quantum Brownian motion, but the discussion does not resolve the original request for references or specific works.

Contextual Notes

The discussion lacks specific references or detailed mathematical treatment of the stochastic Schrödinger equation, and the original poster's request remains unfulfilled.

Alexey
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Dear frends!
Prompt please references to works in which it was considered the Schrödinger 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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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.
 

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