Derivation of the Klein – Gordon – Fock equation from first principles

Abstract

In this paper, the Klein – Gordon – Fock equation is derived from the first principles. There is no need to postulate the existence of wave functions or to axiomatically introduce values of equation coefficients within the framework of the applied approach. The equation was derived on an adiabatically variable manifold, locally described by the FRW metric with complete electrodynamics constructed on it. Here the transverse electromagnetic field (TEMF) is quantized due to the adiabatic change in the metric tensor and the Planck constant acts as an adiabatic invariant of the TEMF. Moreover, the wave functions appear in the equations in a natural way, being eigenfunctions of the Sturm – Liouville problem. These are the functions in which the TEMF function is expanded. To summarize, the proposed approach makes obvious the physical meaning both of the equation itself and of quantum mechanics in general.

Keywords

• klein – gordon – fock equation
• schrödinger equation
• sturm – liouville problem
• quantization of electromagnetic field