  A novel method is presented for implementation of the extended mean-field
theory incorporating two-body collisions. At a given time, stochastic imaginary
time propagation of occupied states are used to generate a convenient basis.
The quantal collision terms, including memory effects, is then computed by a
backward mean-field propagation of these single-particle states. The method is
illustrated in an exactly solvable model. Whereas the usual TDHF fails to
reproduce the long time evolution, a good agreement is found between the
extended TDHF and the exact solution.
