Abstract
We show that the Hermitian Hamiltonian formalism in the paper "Scattering-theory analysis of waveguide-resonator coupling" by Xu [Phys. Rev. E 62, 7389 (2000)] is incompatible with the standard perturbation analysis in a strict sense and hence needs to be used with caution. To improve, a perturbation analysis strictly compatible Hermitian Hamiltonian formalism for modeling the adiabatic time evolution of electromagnetic wave in dielectric medium is outlined. Using a quantum T -matrix based approach, we demonstrate the validity of our Hermitian Hamiltonian formalism and more importantly the effectiveness of the application of quantum formal scattering theory in electromagnetics by exactly rederiving the Rayleigh formula for the total cross section of a nonmagnetic dielectric sphere at the long-wavelength limit.
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