Joint solution of the Klein–Gordon and Maxwell's equations

The article describes the interaction of electromagnetic fields with the quantum-dynamical system, which represents a charged spinless particle moving in some potential created by other charged particles. An example of such a system is an atom, molecule, quantum dot in an external electromagnetic field. For the first time, a system of coupled equations in which the unknown functions are the wave function of a charged particle and the components of electromagnetic fields. The paper will be useful for specialists engaged in the solution of problems of interaction of electromagnetic fields with low-dimensional structures - quantum dots and quantum wells. The resulting system of equations can be used to describe the interaction of low-dimensional structures in a nanoresonator.