The solution must be obtained independently for the two domains "z"<0 and "z>0", where at the domain boundary (z=0) the usual conditions on continuity of the wave function and its derivatives are applied. Since the potential is periodic deep inside the crystal, the electronic wave functions must be Bloch waves here. The solution in the crystal is then a linear combination of an incoming wave and a wave reflected from the surface. For "z">0 the solution will be required to decrease exponentially into the vacuum