Aharonov-Bohm and other cyclic phenomena
type: Item
instance of: scholarly article
title: Aharonov-Bohm and other cyclic phenomena
zbMATH Open document ID: 0899.35082
author: J. Ning
published in: Springer Tracts in Modern Physics
publication date: 1997-12-10T00:00:00Z
review text: The Aharonov-Bohm effect is one of the most surprising quantum mechanical phenomena, till now considered by some authors as a working hypothesis, which predicts that the motion of a charged particle can be influenced by the existence of electromagnetic fields in regions which the particle does not enter. This effect is a simple consequence of applying wave mechanics to electromagnetic theory and is related to the fact that in the wave equation describing the motion of a charged particle in a magnetic field \(\vec B\), not the field appears but the corresponding magnetic potential \(\vec A\) such that \(\vec B=\text{rot }\vec A\), and even if \(\vec B\) is zero, the potential \(\vec A\) may be different from zero which provokes the influence of an ``inexistant'' field on the motion of a charged particle. The purpose of the book under review is ``to discuss the nature of the Aharonov-Bohm effect and to consider also some other effects that are associated with cyclic motion''. The common peculiarity of all phenomena considered in the book is their anholonomy which means that the dynamical state of a system depends not only on phase space coordinates at the current position but also depends on the route by which the system reached this position. The book consists of two parts. The first part (Chaps. 1-7) is a detailed description and explanation of the Aharonov-Bohm effect, its theory and numerous experiments carried out by different researchers. The author discusses the theoretical base of each experiment, the accuracy of corresponding measurements as well as the critical arguments of other scientists. The second part (Chap. 8) contains a description of other phenomena involving movement on a closed circuit and their applications to Larmor precession and accelerator physics.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 00A79
zbMATH DE Number: 1095731
zbMATH Keywords: Aharonov-Bohm effect
zbMATH Keywords: Schrödinger operator
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1095731