# Trouble with normalizing a wave function

1. Apr 29, 2013

### marineric

1. The problem statement, all variables and given/known data
A particle of mass m is in the state ψ(x,t) = Ae-a[mx2/h-bar)+it]

Find A

2. Relevant equations
I know that to normalize a wave function I should use ∫ψ2 = 1

3. The attempt at a solution
The book gives the solution as 1 = 2abs(A)2∫ e-2amx2/h-bar) dx

My question is where does the "2" factor in front of the A2 come from?

2. Apr 29, 2013

### Fightfish

(i) the domain of the wavefunction
(ii) the bounds of that integral

3. Apr 29, 2013

### marineric

i) the domain is for all x and t > 0?

ii) the bounds of the integral are from 0 to ∞

4. Apr 29, 2013

### marineric

I think I got it. The solutions manual integrated from 0 to ∞, and multiplied by 2 because of symmetry (to get the -∞ to 0 part)

5. Apr 29, 2013

### Fightfish

Yup, seems like it. It is rather odd of them to do that though; usually we like -∞ to ∞ bounds because they allow us to use the Gaussian integration formula.