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A Classical intr. ang mom and quantum intr ang mom relation

  1. May 28, 2017 #1
    upload_2017-5-28_21-26-53.png

    Here is a link to a derivation of classical intrinsic angular momentum:

    https://www.scribd.com/document/349675642/Potential-energy-Prop-to-SL

    In 2.1 in the image above they define: ##m=2\mu S## and say that ##\mu## is the bohr magneton. By using the defintion of the bohr magneton I get ##m=2\frac{e \hbar}{2m_e}S=\frac{e \hbar}{m_e}S##. But that is the same as the relation in the classical intrinsic angular momentum derivation except that it has an extra ##\hbar## in the numerator. Anyone who knows how to derive an relation between the classical intrinsic angular momentum relation to magnetic moment and the one with an extra ##\hbar##?
     
  2. jcsd
  3. May 29, 2017 #2
    This is only a matter of units, ##S## as defined on the LHS is dimensionless, where it has the dimension of angular momentum (length*momentum/time) on the RHS. Typically, one includes the ##\hbar## in the definition of quantum spin, as in ##S_z=\frac{\hbar}{2}\sigma_z## with ##\sigma_z## the pauli matrix.
    Interestingly, ##\hbar## can count both as a quantum of action and of angular momentum (probably there's a deep connection, though I can't think of it right now).
     
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