  A method of solving the time-dependent Schr\"odinger equation is presented,
in which a finite region of space is treated explicitly, with the boundary
conditions for matching the wave-functions on to the rest of the system
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 Schr\"odinger 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.
