Riemann surface and quantization

Abstract

This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface corresponding to the multivalent $\operatorname{Ln}\Psi $ function. A visual interpretation of "trajectories" of the quantum system and of the Feynman's path integral is presented. A magnetic dipole having a magnetic charge that satisfies the Dirac quantization rule was obtained.