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Unit Operator

  1. Nov 26, 2006 #1
    Time dependent perturbation theory...

    second order term...

    For some reason they replace

    [tex]<E_{n}|H_{0}^2|E_{m}>[/tex]

    with

    [tex]\Sigma<E_{n}|H_{0}|E_{i}><E_{i}|H_{0}|E_{m}>[/tex]

    I know why they are allowed to do this, what I don't understand is how it makes my life better?
     
  2. jcsd
  3. Nov 27, 2006 #2

    Meir Achuz

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    The fact that \sum|E_i><E_i|=1 is called the completeness property of the states E_i>. It means that you have enough states to expand a function in.
    Look at the fourier sin series. There sin(2pi x/L) form a complete set.
    It becomes useful when the |E_i> are eigenstates of H_0, while the |E_m> are not.
     
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