Introduction to Quantum Mechanics in Four-Dimensional Space Based on the Theory of Space

The article, based on the structure of elementary particles in the form of spatial vortices revealed in the Theory of Space, the four-dimensional structure of space, and the essence of electromagnetic interactions, formulates Hamilton and Hamiltonian-Jacobi functions describing the free motion of an elementary particle and the system of elementary particles in a hydrogen atom, approximating elementary particles with a single spatial vortex. It is shown that the complex nutation and precession of a spatial vortex identified with an elementary particle can be identified with matter waves described by transverse de Broglie plane waves of classical quantum mechanics on the boundary hypersurface βϰβ, which also determines the limit of applicability of classical quantum mechanics, which reduces the complex trajectory of spatial vortices to the analysis of deformations on one of the boundary hypersurfaces.