A method of embedding

A surface potential is derived which can be added to the Schrodinger equation for a limited region of space, I, to embed it into a substrate. This potential, which is energy-dependent and non-local, can be found from the Green function for the bulk substrate. The results are based on a variational principle which gives the energy of a state in terms of the wavefunction in I. The embedded Schrodinger equation can be solved by a basis set expansion, for the wavefunctions of discrete states and the Green function in the continuum, and the method is demonstrated for the case of a square well.