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Homework Help: Vector potential

  1. Apr 18, 2013 #1
    This is not a homework question but I think this is the best place to ask it.

    I was reading a book on quantum mechanics and I came across this expression using the Coulomb gauge in a constant magnetic field,

    [tex]\left(\vec{\nabla}\times\vec{A}\right)_{i} = \epsilon_{ijk}\partial_{j}\left(-\frac{1}{2}\epsilon_{kst}x_{s}B_{t}\right) [/tex]

    But where is the -1/2 coming from?
  2. jcsd
  3. Apr 18, 2013 #2


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    To see it, carry through the exercise of writing out the right hand side for a particular choice of the index ##i##.

    (Alternately, you could make use of one of the identities of the the Levi-Civita symbol; but, if you are just getting familiar with this notation, I think it's a better exercise to expand the right hand side by thinking about the meaning of the symbols.)
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