Abstract
In this paper we generalize the Green's function method which we developed for calculating the surface states in a semi-infinite three-dimensional crystal, to the case of a crystal slab. We only consider the case of one atom in a unit cell as the extension to “complex” crystals (i.e. crystals having more than one atom per unit cell) does not involve any principal difficulty. Applying the method to the case of a simple cubic crystal slab with (100) boundaries, we can show that the maximum number of surface bands in one forbidden gap is given by the number of atomic (100) layers.
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