ABSTRACT
This chapter explores the nonrelativistic approximation here because of the significant similarity in form between nonrelativistic classical mechanics and nonrelativistic quantum mechanics. The transition from classical electrodynamics to quantum electrodynamics in the framework of the Hamiltonian method is then quite similar to the transition from classical mechanics to nonrelativistic quantum mechanics. The transition from classical electrodynamics in Hamiltonian form to quantum electrodynamics is performed in precisely the same way as the transition from classical nonrelativistic mechanics to quantum mechanics. Interestingly, the Hamiltonian method was practically ignored in relation to classical electrodynamics in the past and became popular only after the emergence of quantum electrodynamics. The Hamiltonian method proved to be very convenient for solving a variety of classical problems, particularly those involving a medium. The classical Hamiltonian function of the electromagnetic field in vacuum in the absence of charges is the field energy, but if charges are present then authors must include the energy of their interaction with the field.
