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 $\mathrm{Ln}\Psi$ 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.

32 pages, 7 figures

References in corpus (5)

• On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
• Observation of Dirac Monopoles in a Synthetic Magnetic Field
• Formation of Quantum Shock Waves by Merging and Splitting Bose-Einstein Condensates
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• The properties of the first equation of the Vlasov chain of equations

Cited by in corpus (5)

• $\Psi$ - model of micro- and macrosystems
• Dispersion chain of quantum mechanics equations
• Solution of the nonlinear equation of a divergent type in the corner point domain
• Universal density matrix for the phase space
• The chain of quantum mechanics equations