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Uncertainity relation

  1. Oct 7, 2008 #1
    Show that [A,B] = AB - BA = iqI, where q is a real no. and I is the identity matrix, cannot be satisfied by any finite dimensional Hermitian matrix A and B.

    I think this problem is something related to the uncertainity relation:
    [tex] <(\Delta A)^{2}><(\Delta B)^{2}>\geq \frac{\left|C\right| ^{2}}{4} [/tex]
    but I don't know how to find the variance of A and B .......

    How should I approch this problem? Are there any trick to do with the "finite dimension" ?
  2. jcsd
  3. Oct 8, 2008 #2
    No, the problem has nothing to do with the uncertainty relations. Try taking the trace of both left-hand and right-hand sides of your equation.
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