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Spin 1/2 and 720 degree rotation

  1. Mar 4, 2012 #1
    Hello everybody,

    I was watching a lecture on quantum mechanics, and the lecturer was talking about the 720 degree rotation required for a spin 1/2 particle to return to an identical state. I'm aware of this, but I was more interested in the experiment to show that there is an actual difference.
    He described an experiment where neutrons where fired into the double slit experiment, and one of the beams was rotated 360 degrees, and maxima turned into minima and vise versa.
    My question: how did the experimenters rotate the particles? I could imagine a magnetic field that rotates over distance and the poles on both sides of the apparatus being identical, but I'm not sure if that's the method used.
    So am I right in thinking that, or did they use another method?

    Thanks in advance
  2. jcsd
  3. Mar 5, 2012 #2
    For a particle with spin, its spin axis will precess around a magnetic field line. The rate of its precession depends on the magnetic field strength and the gyromagnetic ratio of the particle. (The gyromagnetic ratio in turn depends on the charge, mass, and g factor.)

    If the spinning particle is in a large magnetic field B0, aligned along the z-axis, its precession rate will be γB0. Interesting things happen when we apply a second, small magnetic field that rotates in the plane perpendicular to B0, but has constant magnitude. The spin axis will precess about the axis of the total field, given by the vector sum of B and B0. When the rotating field is set to rotate at exactly the same rate as the precession rate, the spin will precess in the plane perpendicular to B, i.e. the spin axis will go around a circle passing through the positive and negative z-axis. This scenario is called "paramagnetic resonance." (The z-component of the spin's magnetic field will oscillate with greatest magnitude in this scenario, so this resonant frequency can be determined experimentally.)

    So if you know the paramagnetic resonant frequency of the particle (determined by its gyromagnetic ratio and the magnitude of the total magnetic field), tune your small field B to that frequency. Turn on both of the fields for a short "pulse" that lasts exactly one entire period. This will cause the spin to precess exactly 360 degrees. This is called "pulsed paramagnetic resonance." In your scenario, if you know the speed of the neutrons, you could set up the right size region of magnetic field so that the neutrons pass through for exactly a time of one period.

    A good citation would be Shankar's Principles of Quantum Mechanics (2nd ed), page 392-394.
    Last edited: Mar 5, 2012
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