Continuum Bound States as surface states

We discuss the relation between continuum bound states (CBS) localized on a defect, and surface states of a finite periodic system. We use the transfer matrix method to model an experiment of Capasso, and find all continuum bound and anti-bound states. We compute the rate for intra-subband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.