The virial theorem and the method of multipliers in spectral theory

Abstract

We provide a link between the virial theorem in functional analysis and the method of multipliers in theory of partial differential equations. After giving a physical insight into the techniques, we show how to use them to deduce the absence of eigenvalues and other spectral properties of electromagnetic quantum Hamiltonians. We focus on our recent developments in non-self-adjoint settings, namely on Schroedinger operators with matrix-valued potentials, relativistic operators of Pauli and Dirac types, and complex Robin boundary conditions.