By James Hamilton
The Aharonov-Bohm influence is linked to cyclic movement. it really is one in every of a couple of anholonomic results, and which means the dynamical description is dependent upon the present place of the procedure and at the direction in which it reached that place. An instance of an anholonomic influence is Foucault's recognized pendulum, which easily demonstrates the Earth's rotation. The Sagnac impression - a gentle beam passing round a circled process of mirrors - is one other instance. sleek dynamical advancements resembling Hannay's perspective and Berry's section are extra necessary examples.
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Extra info for Aharonov-Bohm and other Cyclic Phenomena
2. When B = 0 in the solenoid, the intensity observed at Q is where ~i, r are the wave packets (of mean wavelength ~) passing via DI, D2 respectively. 1) 46 5. Problems with, and Criticisms of, Experiments and the AB Effect Itself ~--- a 0 --~ ~176 -'- 'i\' O. x~, :\I V>y Q ) 0 Q Fig. 1. Biprism electron interferences (angles exaggerated) ~176 v ~Y Fig. 2. 1a) It can be seen from Fig. 2, that for 9 > 0 the fringe pattern is shifted to the right. 2) where All is the fringe separation. With the parameters in Fig.
It will be recognised as the cyclotron frequency of classical theory. T h e M e t h o d . In order to find the main features of the motion a simple form of the variational method will be used here. It is known that in general the variational method is better in determining eigenvalues than in finding wave functions, and this also becomes clear here. An exact wave-mechanical solution is not trivial; one is given in Sects. 3 in Appendix H, and the Landau-Lifschitz method is demonstrated in Sect. 1.
Assume t h a t the electron wave packet moves around a circle p = Po lying in the plane z = 0. The wave packet will have a small radial spread about this circle. The minimum value of radial spread, as we saw in Sect. 9c) for the lowest state (n = 0) of radial oscillation. 4a) is used. 9d) shows that we require M to be fairly large in order to give a well-defined orbit even when the lowest value, n = 0, is used. 9d) is to be multiplied by (2n + 1) 1/2 for n > 0. 17) The integration has been taken along the path of the wave packet, starting at 0 = 0.
Aharonov-Bohm and other Cyclic Phenomena by James Hamilton