Bound states of a finite periodic potential

We locate the bound states for a one-dimensional potential which consists of N identical cells, by the transfer matrix method. Our expressions involve only the Bloch phase and a scattering phase, both of which are properties of the single cell. The method applies to an arbitrary but nonoverlapping potential shape, and thereby emphasizes generic properties over specific details. It gives useful qualitative insight without tedious calculations. We discuss the evolution of the bound states as the intercell spacing is varied, and the occurrence of surface states as bound states in a forbidden zone.