Quantum Flux and Reverse Engineering of Quantum Wavefunctions

TL;DR

This paper introduces a novel method for analyzing quantum wavefunctions by extending the flux operator and using a processed Husimi representation to reverse engineer classical structures from quantum data.

Contribution

It develops an extended flux operator using coherent states and introduces a processed Husimi method to deconstruct wavefunctions into classical trajectories.

Findings

Effective in systems with zero or misleading probability flux

Enables visualization of underlying classical dynamics

Demonstrated on quantum wavefunctions to reveal classical structures

Abstract

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent states. We present a "processed Husimi" representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wavefunction, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wavefunction.