Bound states of a finite periodic potential

We locate the bound states for a one-dimensional potential which consists o f 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 p otential shape, and thereby emphasizes generic properties over specific det ails. It gives useful qualitative insight without tedious calculations. We discuss the evolution of the bound states as the intercell spacing is varie d, and the occurrence of surface states as bound states in a forbidden zone . (C) 2000 American Association of Physics Teachers.