Band Spectra of Kronig-Penney Model with Generalized Con- tact Interaction

We extend the standard Kronig-Penney model with periodic δ potentials to the cases with generalized contact interactions under the assumption that the system has time-reversal symmetry. By applying Bloch theorem, the eigenvalue equation which determines the dispersion relation for onedimensional periodic array of the generalized contact interactions is deduced within the framework of the transfer matrix formalism. Some elementary results which indicate a specific nature of the standard model with δ potentials are shown. key words: quantum mechanics, one dimension, Kronig-Penney model, generalized contact interaction, wave function discontinuity, functional analysis