Phase amplitude separation of wave function as local gauge transformation

TL;DR

This paper explores the separation of wave function amplitude and phase as real quantities, linking it to gauge transformations in electrodynamics, to better understand quantum states and their observables.

Contribution

It introduces a novel perspective connecting wave function phase-amplitude separation with local gauge transformations in quantum mechanics.

Findings

Separation of wave function into amplitude and phase is analogous to gauge transformations.

Provides a framework for analyzing quantum states through real quantities.

Highlights the role of gauge invariance in quantum wave functions.

Abstract

A quantum-mechanical wave function is complex, but all observations are real, expressible through expectation values and transition matrix elements that involve the wave functions. It can be useful to separate at the outset the amplitude and phase as real quantities that together carry the same information that is contained in the complex wave function. Two main avenues for doing so go way back in the history of the subject and have been used both for scattering and bound states. A connection is made here to gauge transformations of electrodynamics where the advent of quantum mechanics and later quantum field theory showed the central role that local gauge transformations play in physics.