Using the example of a non-uniform electromagnetic wave created by superposition of two plane monochromatic electromagnetic waves that are arbitrarily directed relative to each other, an approach is demonstrated that allows one to simulate a wide spectrum of electromagnetic waves. The complete system of equations describing the motion of an electron in a non-uniform electromagnetic field is solved numerically. The features of the trajectory and emission spectrum of the electron were found and investigated.
The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.
Quantum Dynamics and Non-Inertial Frames of Reference. III: Charged Particle in Time-Dependent Uniform Electromagnetic Field