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Seeking Text On Distributions

  1. Nov 29, 2004 #1
    Hi, I am not seeking a "complete" treatment of distribution functions (like Gelfand or Schwartz). However, I would like some discussion in regards to multiplying delta functions together---especially in QM.

    From the little I have discovered, distributions do not form an algebra, and thus, one cannot "legally" multiply delta functions together. However, we do this all the time:

    [tex]
    \delta(\mathbf{r}-\mathbf{r}_0) = \delta(x-x_0)\delta(y-y_0)\delta(z-z_0)
    [/tex]

    Also, I was wondering about a text that discussed in detail the problem with "complete" sets of eigenfunctions in an infinite-dimensional space ([itex]L_2[/itex]) and normalizing to a delta function rather than to 1. I guess I am looking for better explanations than the typical "it just works" explanation. Do I need von Neumann's book?

    Thanks.
     
  2. jcsd
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