Normalize Wave Function: Find A Value

[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?

 

[Gokul43201]

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.

 

[CollectiveRocker]

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

 

[Gokul43201]

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

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