The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been used since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential. Likewise, in a Stern–Gerlach experiment, a charged particle is modeled as a quantum system, while the background magnetic field is described classically. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles.
the full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems a simpler approach one that has been used since the inception of quantum mechanics is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field for example the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical coulomb potential likewise in a stern–gerlach experiment a charged particle is modeled as a quantum system while the background magnetic field is described classically this "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role such as in the emission of photons by charged particles