von Neumann-Landau equation for wave functions, wave-particle duality and collapses of wave functions

TL;DR

This paper introduces a von Neumann-Landau equation framework that models quantum wave functions, providing a formalism for wave-particle duality, and interprets wave function collapse as a transition between multiple levels and a single state.

Contribution

It develops a mathematical formalism using bipartite wave functions to describe quantum motion and duality, extending Schrödinger's equation and offering a new perspective on wave function collapse.

Findings

von Neumann-Landau equation formalism models quantum dynamics

Wave-particle duality is expressed through bipartite wave functions

Wave function collapse is viewed as a transition from many levels to one

Abstract

It is shown that von Neumann-Landau equation for wave functions can present a mathematical formalism of motion of quantum mechanics. The wave functions of von Neumann-Landau equation for a single particle are `bipartite', in which the associated Schr\"{o}dinger's wave functions correspond to those `bipartite' wave functions of product forms. This formalism establishes a mathematical expression of wave-particle duality and that von Neumann's entropy is a quantitative measure of complementarity between wave-like and particle-like behaviors. Furthermore, this extension of Schr\"{o}dinger's form suggests that collapses of Schr\"{o}dinger's wave functions can be regarded as the simultaneous transition of the particle from many levels to one.