Complemetarity of Phases in Aharonov-Bohm Solenoid Effect

TL;DR

This paper proposes a complementarity principle linking phase calculations in the Aharonov-Bohm effect, suggesting that the sum of phase changes around the system should cancel, ensuring consistency between different phase calculations.

Contribution

It introduces a new complementarity concept between phase calculations in the Aharonov-Bohm effect, unifying different approaches under a compatibility condition.

Findings

The sum of phase changes around the system should vanish.

A compatibility relation between different phase calculations is established.

The approach ensures consistency in the Aharonov-Bohm phase analysis.

Abstract

In the present Note it is suggested that there should be a certain complementarity of phases between Aharonov-Bohm (AB) solenoid phase calculation on one part of the system and a phase calculation about another part of the physical system. Assuming a unique value for the function of the total system, after a complete circulation of the electron around the solenoid, the sum of these two phase changes should vanish. Such assumption leads to a compatibility relation between our previous calculations for the AB solenoid phase effect and that of the original calculation by AB.