Time-evolution of metamaterial strings

This Bachelor project deals with the time evolution of metamaterial strings governed by the Schrodinger equation. From the Maxwell's equations we derive a theoretical model for the setting of simultaneously negative permitivitty and permeability. A mathematical rigorous framework is inspired by quantum mechanics and leads to an unbounded self-adjoint operator in a Hilbert space with nonstandard interface conditions. We derive an implicit equation for its eignevalues and corresponding eigenfunctions and implement a numerical scheme for computing them to double precision. Given an arbitrary initial datum, the Schrodinger equation is solved by using the Fourier decomposition in terms of the eigenbasis of the self-adjoint operator.