Quantum Phase and Quantum Phase Operators: Some Physics and Some History

TL;DR

This paper reviews the development and physics of quantum phase operators, examining their theoretical foundations, historical context, and recent proposals, while addressing key questions about their uniqueness and physical realizability.

Contribution

It provides a historical analysis of quantum phase operators and critically evaluates recent proposals, clarifying unresolved issues in the field.

Findings

Quantum phase operators have a complex development history.

There are unresolved questions about the uniqueness of quantum phase operators.

Recent proposals offer new insights but require critical assessment.

Abstract

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.