The one particle theory of periodic point interactions

We solve explicitly and without approximation the problem of a quantum-mechanical particle inR ³ subjected to point interactions that are periodic inR ³ with periodicity of the typeZ, Z ², andZ ³. In the first case we get a model of an infinite straight polymer, in the second case we get a model of a monomolecular layer and in the third case we get a model of a crystal. In all three cases the unit cell of the Bravais lattice is allowed to contain any finite number of interaction sites (atomes), placed arbitrarily and with arbitrary interaction strength. In the case: one interaction site per unit cell we find explicit formulas for the resonance bands and energy bands and their corresponding wavefunctions.