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

Abstract

Solutions of the one-dimensional Schrödinger 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.