Norm of resonance states in quantum scattering and electromagnetic systems

Abstract

Resonance states spatially diverge and are thus not square integrable. Instead, their norm is defined by the biorthogonal scalar product of left and right states. We replace the corresponding volume integral by a convenient boundary integral in piecewise homogeneous systems and apply this procedure to diverse physical settings. For a quantum particle in any number of dimensions we treat hard-wall and piecewise constant potentials. For electromagnetic systems with piecewise homogeneous material properties, we consider three-dimensional and effectively two-dimensional cavities of arbitrary shape. As examples, we treat the spherical scatterer and the circular disk.