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Functions of time 0?

  1. Aug 23, 2013 #1
    Hi Guys,

    In a lot of books dealing with spectroscopy, correlation functions or any kind of functions involving time sometimes take the form like this:

    [itex]\left\langle A[q,u(t)]A^{*}[q,u(o)] \right\rangle[/itex]

    Where [itex]A[/itex] is some function that depends on say [itex]q[/itex] and [itex]u[/itex], and [itex]u[/itex] is another function that depends on time [itex]t[/itex].

    What is the physical significance of the multiplication by its conjugate at time [itex]t = 0[/itex]?

  2. jcsd
  3. Aug 23, 2013 #2


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    Science Advisor

    It would probably have been clearer if it was written
    [itex]\left\langle A[q,u(t_0+t)]A^{*}[q,u(t_0)] \right\rangle[/itex]

    The average is over ##t_0##.
  4. Aug 23, 2013 #3
    Hmm does that mean if i was trying to work out one of these equations for say a series of 5 ##t_0## values eg ##[1, 2, 3, 4, 5]##, does that mean for ##t_3## I would do
    [itex]\left\langle A[q,u(3)]A^{*}[q,u(1)] \right\rangle[/itex], or
    [itex]\left\langle A[q,u(3)]A^{*}[q,u(0)] \right\rangle[/itex] or
    [itex]\left\langle A[q,u(3)]A^{*}[q,u(2)] \right\rangle[/itex]

    and similarly for the next time ##t_4## eg...

    [itex]\left\langle A[q,u(4)]A^{*}[q,u(1)] \right\rangle[/itex], or
    [itex]\left\langle A[q,u(4)]A^{*}[q,u(0)] \right\rangle[/itex] or
    [itex]\left\langle A[q,u(4)]A^{*}[q,u(3)] \right\rangle[/itex]

    Thanks for your time.
    Last edited: Aug 24, 2013
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