Remarks on magnetic and electric Aharonov-Bohm effects

TL;DR

This paper provides direct proofs and experimental proposals for magnetic, electric, and gravitational Aharonov-Bohm effects, along with a new inverse problem for Schrödinger equations, advancing understanding of quantum phenomena without relying on scattering theory.

Contribution

It offers a direct proof framework for AB effects, proposes experimental setups, and introduces a novel inverse problem related to time-dependent Schrödinger equations.

Findings

Direct proof of magnetic AB effect without scattering theory

Proposed physical experiments for magnetic and electric AB effects

Introduction of a new inverse problem for Schrödinger equations

Abstract

We give a direct proof of the magnetic Aharonov-Bohm effects without using the scattering theory and the theory of inverse boundary value problems. This proof can serve as a framework for a physical experiment to confirm the magnetic AB effect. We prove also the electric AB effect and we suggest a physical experiment to demonstrate the electric AB effect. In addition, we consider a combined electric and magnetic AB effect and we propose a new inverse problem for the time-dependent Schr\"odinger equations. Finally we study the gravitational AB effect.