The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum system. However, the Schrödinger equation itself is not directly applicable to Quantum Electrodynamics (QED), which is the quantum field theory describing the electromagnetic force.
In QED, the dynamics of the electromagnetic field and its interactions with charged particles are described using a different mathematical framework called quantum field theory. The basic equations of QED are formulated using the principles of special relativity and quantum mechanics.
The key equation in QED is the Dirac equation, which describes the behavior of fermionic particles (such as electrons) in the presence of the electromagnetic field. The Dirac equation combines quantum mechanics and special relativity and provides a relativistic description of the behavior of fermions.
The Dirac equation includes the interaction between the fermionic particle and the electromagnetic field through the coupling to the electromagnetic potential. The electromagnetic potential is described by the four-vector potential, which combines the scalar potential and vector potential.
To fully describe the dynamics of quantum electrodynamics, the Dirac equation is combined with the equations describing the behavior of the electromagnetic field, namely Maxwell's equations. Maxwell's equations govern the propagation and behavior of the electromagnetic field and include the effects of charged particles.
The full mathematical description of QED involves the use of quantum field theory techniques, including Feynman diagrams and perturbation theory, to calculate scattering amplitudes and interaction probabilities for particles interacting through the electromagnetic force.
In summary, while the Schrödinger equation is not directly applicable to QED, the behavior of fermionic particles in QED is described by the Dirac equation, which incorporates the interaction with the electromagnetic field described by Maxwell's equations.