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

1. Dec 18, 2012

1. The problem statement, all variables and given/known data

Consider the Gaussian Distribution

$ρ(x) = A e^{-λ(x-a)^{2}}$

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

2. Relevant equations

$\int^{∞}_{-∞}ρ(x) dx = 1$

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 $A = \sqrt{\frac{λ}{π}}$. 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. Dec 18, 2012

### TSny

3. Dec 18, 2012