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Spin density matrix

  1. Aug 10, 2009 #1
    Could any one help me to understand how the spin density matrix is invariant under unitary transformation?
  2. jcsd
  3. Aug 12, 2009 #2
    if you mean how a general density matrix is invariant under unitary transformation, the consider that density matrices are used to evaluate mean values of an operator A, <A R>= Tr(AR), where R is the density matrix and Tr denotes the trace operation. Then performing a unitary transformation yields the same result: Tr(SAS^-1 SRS^-1) = Tr(SARS^-1) = Tr(S^-1SAR) = Tr(AR) because of invariance under cyclic permutation of the trace.
    If you mean something else, please forget my answer and post again.
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