Algorithm of the numerical decision of stochastic Shrodinger equation.

[Alexey]

Prompt please where it is possible to find algorithm of the numerical decision of stochastic Shrodinger equation with casual potential having zero average and delta – correlated in space and time?

 

The equation:

i*a*dF/dt b*nabla*F-U*F=0

 

where

i - imaginary unit,

d/dt - partial differential on time,

F=F (x, t) - required complex function,

nabla - Laplas operator,

U=U (x, t)- stochastic potential.

Delta-correlated potential <U(x,t)U(x`,t`)>=A*delta(x-x`) *delta(t-t`) .

where delta - delta-function of Dirack, A – const, <> - simbol of average,

Zero average: <U(x,t)>=0

Gaussian distributed P(U)=C*exp(U^2/delU^2)

Where C, delU - constants.