By Professor Dr. Joachim Kessler (auth.)

ISBN-10: 3662127210

ISBN-13: 9783662127216

ISBN-10: 3662127237

ISBN-13: 9783662127230

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We will only explain the essential ideas and emphasize the physical background. Let us first consider the case in which the spin of the incident beam is in the + z direction which we take as the quantization axis. 47) where pI(lJ) are associated Legendre functions;

30), that As E = mye 2 (with y = 1/(Jl - f32) and we get = -1 Y = J-1 - f32. 34) Thus the polarization depends on the reference system; for an unambiguous definition it is therefore practical to refer it to the rest frame. 2]. For our purposes, however, the definition as the expectation value of the spin operator in the rest frame suffices. To conclude, we summarize what the Dirac equation describes: a) Relativistic electrons (although it has not been shown here that the theory is Lorentz invariant, it appears plausible as it started from the relativistic energy equation), b) the spin 1/2 of electrons, c) the magnetic moment eh/2me of electrons, d) spin-orbit coupling.

K 2 • Otherwise this component would define a certain screw sense (helicity) in the laboratory system, for example, a right-handed screw, p. kl > o. With the reflection of the experiment (see Fig. 12) one would obtain a left-handed screw, p. k2 < O. This is because the sense of rotation connected with the polarization is retained with the reflection, whereas the momentum direction kl is inverted. Hence, with the same initial state, the mirror image yields a different final state. This can clearly be seen if one thinks of the image as p r{)~ k'i Fig.

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Polarized Electrons by Professor Dr. Joachim Kessler (auth.)


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