In present work, the Klein-Gordon-Fock equation is obtained from first principles. Within the framework of the applied approach, there is no need to postulate the existence of wave functions, nor to axiomatically introduce values of coefficients of the equation. The equation is derived on an adiabatically variable manifold, locally described by the Friedman-Robertson-Walker metric and with complete electrodynamics constructed on it. In this case, the transverse electromagnetic field is quantized due to the adiabatic change in the metric tensor, and the Planck constant is an adiabatic invariant of the transverse electromagnetic field propagating over the adiabatically changed manifold. Following this approach, the wave functions appear in the equations in a natural way (they are eigenfunctions of corresponding the Sturm-Liouville problem) and these are the eigenfunctions where the function of the transverse electromagnetic field is expanded. For this reason, the axiomatic introduction of wave functions, as well as the postulation of the values of the coefficients in the equation are no longer required. This makes obvious both the physical meaning of the equation itself and quantum mechanics as well.