Trouble with normalizing a wave function

[marineric]

Homework Statement

A particle of mass m is in the state ψ(x,t) = Ae^{-a[mx2/h-bar)+it]}

Find A

Homework Equations

I know that to normalize a wave function I should use ∫ψ² = 1

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?

 

[Fightfish]

Hmm...could you perhaps provide a little more information on
(i) the domain of the wavefunction
(ii) the bounds of that integral

 

[marineric]

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

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

 

[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)

 

[Fightfish]

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)

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.