  Here, we present an overview of recent developments in the characterization
of electromagnetic and quantum metamaterials using effective medium methods. It
is highlighted that both electromagnetic and electronic systems can be
homogenized in a unified manner based on the introduction of an effective
Hamiltonian operator that describes the time evolution of the macroscopic
initial states as well as the stationary states of the relevant system.
Furthermore, it is shown that in some circumstances quadratic forms of the
fields, such as the energy, can be exactly determined using the effective
medium theory.
