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 dipole approximation, with a laser pulse. These conditions are imposed on a surface (boundary) which is usually chosen at a finite (but sufficiently remote) distance from the atom where the motion of electrons can be assumed to be semiclassical. For the numerical integration of the Schrodinger equation, these boundary conditions may be used to replace mask functions and diffuse absorbing potentials applied at the edge of the integration grid. These 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 allows one to reduce significantly the size of the space domain needed for numerical integration; Considering the numerical solution for a one-dimensional model, we demonstrate the effectiveness of our approach in comparison with some other numerical methods. [S1050-2947(99)10412-8].