  The easiest way to quantize the electromagnetic (or: radiation) field consists of two steps. First, one Fourier analyses the vector potential of the classical field into normal modes (using periodic boundary conditions) corresponding to an infinite but denumerable number of degrees of freedom. Second, since each mode is described independently by a harmonic oscillator equation, one can apply the harmonic oscillator treatment from non-relativistic quantum mechanics to each single mode. The result for the Hamiltonian of the radiation field is