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Finding the Normalization Constant of a Gaussian Distribution (Griffiths 1.6)

  1. Dec 18, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the Gaussian Distribution

    [itex]ρ(x) = A e^{-λ(x-a)^{2}}[/itex]

    where A, a, and λ are constants. Determine the normalization constant A.

    2. Relevant equations

    [itex]\int^{∞}_{-∞}ρ(x) dx = 1[/itex]

    3. The attempt at a solution

    The problem recommends you look up all necessary integrals, so I did and I think that I've got it correct. I found that [itex]A = \sqrt{\frac{λ}{π}} [/itex]. My question, if this answer is correct, is just: how do you do this integral? Do you have to actually do some kind of change of variables to a different coordinate system?
     
  2. jcsd
  3. Dec 18, 2012 #2

    TSny

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  4. Dec 18, 2012 #3
    Thanks a bunch. I was a little confused because the solution I had found involved erf and I wasn't quite sure how to use it since I'd never seen that function before.
     
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