Five-dimensional approaches and the theory of the hydrogen atom

The O(4) symmetry of the Schr$\stackrel{..}{o}$dinger equation for the hydrogen atom discovered by Fock, is discussed. The difficulties of physical interpretation of the result using the Fock procedure for determining the stereographic projection in momentum space is indicated. A generalization of the stereographic projection is suggested such that the O(4) symmetry of the hydrogen atom has a clear physical interpretation within the framework of a unified five-dimensional theory of gravitation, electromagnetism, and charged matter. In passing, the problem of the form of the dependence on the fifth coordinate in the given theory is solved.