By Alexander of Aphrodisias, William E. Dooley

ISBN-10: 0801422353

ISBN-13: 9780801422355

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**Extra info for Alexander of Aphrodisias on Aristotles Metaphysics 1. Translated by W. E. Dooley**

**Example text**

The transition probability P−+ = ω12 sin2 [(ω0 − ω ˜ )b/(2v)] 2 (ω0 − ω ˜) , which has a width of the order of b/v but is centered at ω ˜ = ω0 ⇒ ω = ω0 1 − v/c ω0 (1 + v/c) . 2, we ﬁnd that the resonance frequency is displaced: The neutron moves in the propagation direction of the ﬁeld, and there is a ﬁrst order Doppler shift of the resonance frequency. 6. If the neutron beam has some velocity dispersion, the experimental result will be the same as calculated above, but smeared over the velocity distribution.

The experimental measurement of I2 − I3 as a function of the applied ﬁeld B0 is given in Fig. 6. A numerical ﬁt of the curve shows that the distance between two maxima is ∆B = (64 ± 2) × 10−4 T. Fig. 6. 3 with this experimental result, and recalling the result of a measurement of µx for these values, explain why this proves that the state vector of a spin-1/2 particle changes sign under a rotation by an odd multiple of 2π. 1. The beams ABDC2 and ACDC2 interfere. Omitting the propagation factors, one has, at C2 an amplitude A2 = α2 β + β 3 = β(α2 + β 2 ) .

3 simplify in that case? 3 The Stern–Gerlach Experiment Between the slit, whose center is located at the origin (x = y = z = 0), and the detector, located in the plane x = L, we place a magnet of length L whose ﬁeld B is directed along the z axis. The magnetic ﬁeld varies strongly with z; see Fig. 3. We assume that the components of the magnetic ﬁeld are Bx = By = 0 Bz = B0 + b z . In what follows we choose1 B0 = 1 T and b = 100 T/m. 1 This form violates Maxwell’s equation ∇ · B = 0, but it simpliﬁes the following Bz over calculation.

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