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Yes/no question about non-commuting Hermitian operators

  1. Jun 2, 2013 #1

    nomadreid

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    Is the following a theorem? yes or no
    If A and B are non-commuting Hermitian operators (or matrices), there does not exist Hermitian operators C and D such that AB-BA = CD.
    (Or, as special case, ....there does not exist a Hermitian operator C s.t. C= AB-BA)
    Thanks
     
  2. jcsd
  3. Jun 2, 2013 #2

    fzero

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    If A and B are Hermitian, then AB-BA is anti-Hermitian, (##M^\dagger = - M##). ##i(AB-BA)## is therefore Hermitian.
     
  4. Jun 2, 2013 #3

    nomadreid

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    fzero: Thank you very much.
     
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