Alexey
Jul20-03, 02:30 PM
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.
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.