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.

 

[heumpje]

Not sure if this is what you're looking for...

Quantum Monte Carlo methods are used to solve high dimensional integrals... In Diffusion Monte Carlo (DMC), one rewrites the Schrödinger equation in Integral form. This integral is then solved stochastically.