Abstract
In this paper we develop a Green function method, which can be considered as a generalization of the Kohn and Rostoker method, and which enables us to calculate the surface states in a semi-infinite three-dimensional crystal. We only consider the case of one atom in a unit cell, the extension to complex crystals being straightforward. We do not only demonstrate the existence of two-dimensional energy bands localized at the surface and superimposed on the three-dimensional bandstructure of the bulk, but we derive formulae which can be used for practical calculations if one has the disposal of high speed computers with large capacity.
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