By G. N. Afanasiev (auth.), G. N. Afanasiev (eds.)
Among the topics coated during this quantity are the topological results of quantum mechanics, together with Bohm-Aharonov and Aharonov-Casher results and their generalisations; the toroidal moments, anapoles and their generalisations; the numerical research of Tonomura experiments trying out the principles of quantum mechanics; the time-dependent Bohm-Aharonov impact, the thorough learn of toroidal solenoids and their use as potent transmitters of electromagnetic waves; and the topical questions of the Vavilov-Cherenkov radiation. in addition, concrete recommendation is given for the development of magnetic and electrical solenoids and the functionality of experiments at the Bohm-Aharonov influence. additionally, homes of exceptional charge-current configurations and sensible purposes are studied.
Audience: This quantity can be of curiosity to postgraduate scholars and researchers facing new potent resources of electromagnetic waves.
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Extra resources for Topological Effects in Quantum Mechanics
Sample text
O''YI-I coth Vo sin 0 f(v, vo), is defined as follows: f(v,vo) ={ exp( -v) sinh Vo for v > vo, exp(-vo) sinh v for v < Vo. We now evaluate the strengths of the EMF corresponding to the potentials vo), 0'1-1 cosh Vo sinh Vo (_ ) exp(-2v) - cos 20 'Y-'Y R cosh 2v - cos 20 ' 8
5) 36 CHAPTER 3. ELECTROMAGNETIC PROPERTIES OF STATIC SOLENOIDS Let div M = o. , inside the solenoid). We conclude that to construct the static regions where M magnetic solenoid of an arbitrary geometrical form it is enough to fill this form with a substance having divergence-free magnetisation [56). An example is a closed uniformly magnetised filament of arbitrary shape. The magnetised rings used in Tonomura's experiments [21] testing the B-A effect are the particular realisations of such a magnetised filament.
Thus when a solenoid moves in a medium the strengths of the EMF extend beyond the solenoid if ('1-1 oj; 1, and they remain enclosed within it if ('1-1 = 1. 3·8 Generalised Helmholtz Coils and All That These considerations were initiated by the papers [76,77,78] which appeared recently and are devoted to the study of the electromagnetic properties of so called Helmholtz coils. However, it has remained unclear to us whether the cancellation of a particular multipole is a curious, yet isolated, fact or is a manifestation of something more general.