Towards Modelling QFT in Real Metamaterials: Singular Potentials and Self-Adjoint Extensions

Solutions of the one-dimensional Schrodinger equation are found when point interactions of the type aδ(x − q) + bδ'(x − q) are placed either in a couple of points or in a regular lattice. The results obtained in the present study are a first step toward a rigorous mathematical model of real metamaterials is Solid State Physics.