Interaction of the Dirac Electron Located in a Potential Well with a Plane Wave Field

Relativistic physics is the physics of high speeds and energies. The interaction of relativistic particles in the general case does not preserve the rest mass, therefore, the processes of birth, annihilation, and interconversion of particles be-come possible. So, in nucleon collisions, π-mesons are born, the electron and positron, annihilating, turn into γ-quanta. The electric field surrounding a charged particle is the result of the continuous production and absorption of virtual photons. The Schrödinger equation does not describe the possibility of the creation and destruction of particles; moreover, its Hamiltonian corresponds to nonrelativistic classical mechanics. All this means that the Schrödinger equation is valid only in the nonrelativistic field of motion and is not applicable in the relativistic one. This leads to the need to replace the Schrödinger equation relativistically in-variant equation for an electron, Dirac equation. The main task of the relativistic theory is to calculate the probabilities of transitions (scattering cross sections) in a system of free microparticles before and after the interaction, that is, in calculating the result of the interaction. This problem is solved on the basis of non-stationary perturbation theory methods.