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Validity of virial theorem in QM

  1. Aug 24, 2010 #1
    In the standard derivation of the virial theorem, one assumes to be working in the energy basis. One then gets <T> = n/(n+2) <H>. This relation doesn't hold for the continuous spectrum of Coulomb potential where <T> > 0, <H> > 0, n/(n+2) = -1. So, where in the derivation did we use the fact we were dealing with bound states?
  2. jcsd
  3. Aug 25, 2010 #2


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    If I remember correctly, the relation is based on evaluation of the term
    [tex] \langle [H,\mathbf{pr}]\rangle=(E-E) \langle \mathbf{pr}\rangle [/tex].
    In the case of bound states, (E-E)=0 and [tex] \langle \mathbf{pr}\rangle [/tex] is finite. In the case of continuum states, the last average diverges, so that one cannot conclude that the whole expression vanishes.
  4. Aug 25, 2010 #3
    Oh, I see - Thank you!
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