On the integrability of the wave propagator arising from the Liouville-von Neumann equation

TL;DR

This paper investigates the integrability of the wave propagator derived from the Liouville-von Neumann equation, which models quantum density matrices as wave functions, offering new insights into quantum dynamics.

Contribution

It demonstrates the integrability of the wave propagator associated with the Liouville-von Neumann equation in an extended wave function framework.

Findings

Proves the integrability of the wave propagator

Connects the Liouville-von Neumann equation to wave function dynamics

Provides a mathematical foundation for extended quantum wave equations

Abstract

The Liouville-von Neumann equation describes the change in the density matrix with time. Interestingly, this equation was recently regarded as a wave equation for wave functions but not a equation for density functions. This setting leads to an extended form of the Schr\"odinger wave equation governing the motion of a quantum particle. In this paper we obtain the integrability of the wave propagator arising from the Liouville-von Neumann equation in this setting.