Time-dependent embedding

A method of solving the time-dependent Schrodinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wavefunctions to the rest of space replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schrodinger equation. Results are presented for a one-dimensional model of an atom in a time-varying electric field, the surface excitation of this model atom at a jellium surface in an external electric field, and the surface excitation of a bulk state.