Relativistic Kronig-Penney-type Hamiltonians

The relativistic Kronig-Penney model is extended to a wide class of point interactions introduced in the nonrelativistic case by Paul Chernoff and the author. A generalized Kronig-Penney relation, which converges to the standard Kronig-Penney relation in the nonrelativistic Limit, is shown to determine the spectrum of the corresponding Hamiltonian. Several examples are considered, including the well-known special cases of electrostatic and Lorentz scalar point interactions, as well as several new solvable models.