# Normalization Question

1. Nov 11, 2004

### CollectiveRocker

How do I find the value of the normalization constant A for the wave function
Ψ = Axe ^ (-x squared/2)? I know that I set it equal to 1, but do i do the integral from negative infinity to positive infinity; for no other limits are given?

2. Nov 11, 2004

### Gokul43201

Staff Emeritus
Sounds like this very same question has been asked before...that time with the square of the W.f'n. being the given qty...

Yes, if unspecified, integrate from negative to positive infinity.

3. Nov 11, 2004

### CollectiveRocker

So do I just end up with: ((-x squared)/2)Axe ^(-x squared/2), evaluated from negative infinity to infinity?

4. Nov 12, 2004

### Gokul43201

Staff Emeritus
No, you want to find A from
$$\int_{-\infty}^{\infty} \psi ^* (x) \psi (x) dx = 1$$

$$=> \frac{1}{|A|^2} = \int_{-\infty}^{\infty} x ^2 e^{-x^2} dx$$

Last edited: Nov 12, 2004