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Off diagonal element of density matrix

  1. May 14, 2009 #1

    KFC

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    For two level system , let denotes the ground state as 1 and exctied state as 2, for writing the office off-diagonal matrix element for the density operator, shall it be

    [tex]\rho_{12} = |2\rangle\langle 1|[/tex]

    and

    [tex]\rho_{21} = |1\rangle\langle 2|[/tex]

    ???
     
  2. jcsd
  3. May 15, 2009 #2

    naima

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    Gold Member

    From a pure state f = a|0> + b|1> one gets the density opérator
    (a|0> + b|1>)(a*<0| + b*<1|)
    with a off diagonal part ab*|0><1|
    the off diagonal matrix element is ab* = <f |0><1|f> (with |0> and |1> orthogonal)
    With a mixture of pure state f1,f2 with probabilities p1, p2
    we get p1<f1 |0><1|f1> + p2<f2 |0><1|f2>
    I hope there is no error in my answer!
     
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