Miren Zubeldia

The Forward Problem for the Electromagnetic Helmholtz Equation Miren Zubeldia

The magnetic Schrödinger operator is a Hamiltonian which appears in quantum mechanics, for instance in the study of bound states and scattering of particles. It also serves as a mathematical model for other situations, and understanding its properties has been instrumental in the study of various dispersive equations such as wave equation or Schrödinger equation. The direct or forward scattering problem related to this operator consists of proving existence and uniqueness of solution of the associated electromagnetic Helmholtz equation as well as of showing the existence of the scattering amplitude of the solution which characterizes its behavior at infinity. This book contains the study of the direct problem of such an equation for potentials that decay at infinity, but also have singularities at the origin. It is suitable for graduate students and researcher in mathematics interested in the Helmholtz equation with electric and magnetic potentials.