1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Homework Helper
    Gold Member
    2017 Award

  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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook