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Intuition behind Green's function (one dimension)

  1. Sep 30, 2013 #1
    I am studying scattering from these notes.
    There I came across Green's function in one dimension which is computed as
    \langle x|G_o|x'\rangle = -\frac{iM}{\hbar ^2k}\exp(ik|x-x'|)
    I understand Green's function as a sort of propagator from [itex]x'[/itex] to [itex]x[/itex]. There are two observations that can be made for this Green's function (leaving aside the oscillatory dependence)
    1) More the momentum, less the amplitude to traverse from one point in space to other.
    2) Amplitude is independent of the displacement.

    Whereas in 3 dimension it is quiet opposite. The amplitude is independent of the momentum but inversely dependent on displacement.

    Why is this so?
    Last edited: Sep 30, 2013
  2. jcsd
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