Integral boundary conditions for the time-dependent Schrodinger equation: Atom in a laser field

We formulate exact integral boundary conditions for a solution of the time- dependent Schrodinger equation that describes an atom interacting, in the d ipole approximation, with a laser pulse. These conditions are imposed on a surface (boundary) which is usually chosen at a finite (but sufficiently re mote) distance from the atom where the motion of electrons can be assumed t o be semiclassical. For the numerical integration of the Schrodinger equati on, these boundary conditions may be used to replace mask functions and dif fuse absorbing potentials applied at the edge of the integration grid. Thes e latter are usually introduced in order to (approximately) compensate for unphysical reflection which occurs at the boundary of a finite region if a zero-value condition is imposed there on the solution. The present method a llows one to reduce significantly the size of the space domain needed for n umerical integration; Considering the numerical solution for a one-dimensio nal model, we demonstrate the effectiveness of our approach in comparison w ith some other numerical methods. [S1050-2947(99)10412-8].