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Re: electron magnetic moment



Justin Parke wrote:

What is the force of constraint on a spinning electron?
It has a dipole moment and a potential energy when it's
in a magnetic field

1) If we can start from the assumption that the electron
has a built-in spin, then the built-in magnetic moment is
a natural consequence. The correct result differs by a
factor of 2 from what you would get from a macroscopic
classical rotating charged object, but this is spectacularly
well explained by the Dirac equation....
http://scienceworld.wolfram.com/physics/GyromagneticRatio.html

2) So we are left with the question of why the electron
has a built-in spin.

2a) It is fairly easy to see why _orbital_ angular momentum
is quantized in units of hbar. Consider the Bohr model of
the atom, with an electron orbiting the nucleus like a planet
around the sun. The wavelength of the wavefunction depends
on momentum, and you need an integral number of wavelengths
along the circumference i.e. the path of the orbit.

For atoms more complicated than hydrogen the Bohr model
doesn't work too well, but the basic idea of needing an
integral number of wavelengths remains valid.

2b) Spin angular momentum is quantized in units of _half_ hbar.
This is related to the fact that rotating a fermion by 360
degrees does not return the wavefunction to its original
value; it picks up a factor of -1. You have to rotate it
by 720 degrees to get back where you started. Before you
say "that's weird" remember that there are a few situations
in the macroscopic classical world where a 720 degree rotation
is required:
http://mailgate.nau.edu/cgi-bin/wa?A2=ind0105&L=phys-l&P=R9774

The only slightly puzzling thing is why there are so many
classical situations where you can "get away with" only a
360 degree rotation.