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Propagator equation

  1. Aug 4, 2007 #1
    I understand the progator in general but could someone explain this equation for the propagator at t = 0 for me:

    [tex]\delta(x' - x) = K(x',x;0,0) = \sum_m \psi_n(x')\psi_n(x)[/tex]

    ?

    I am confused about the dfiference between x' and x. It seems like the Kronecker would make more sense than Dirac here?
     
  2. jcsd
  3. Aug 4, 2007 #2

    Gokul43201

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    x is continuous.
     
  4. Aug 4, 2007 #3
    And x' is discrete? What do they represent?
     
  5. Aug 4, 2007 #4

    Gokul43201

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    No, x and x' are both positions. They (and t, t') are continuously varying parameters; hence the Dirac delta.

    The propagator K(x,x';t-t') is the amplitude for a particle initially at (x',t') to be observed at (x,t). With t=t', this is the probability amplitude that a particle at x' is also at x, which is given by the Dirac delta distribution.
     
    Last edited: Aug 4, 2007
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