# Homework Help: Normalized Wave-Function

1. Jun 4, 2012

### karkas

1. The problem statement, all variables and given/known data
Its simple, I've encountered this problem in Beiser's book and it doesn't seem right:

Prove that the function $$R_{10}(r) = \frac{2}{a_{0}^{3/2}}\cdot e^{-\frac{r}{a_0}}$$ is normalized.

2. Relevant equations
$$\int_{-\infty}^{\infty} |\psi|^2 dV = 1$$

3. The attempt at a solution
I figured it's simply just taking the integral
$$R_{10} (r)=\int^{\infty}_{0}( \frac{2}{a_{0}^{3/2}}\cdot e^{-\frac{r}{a_0}})^2dr = 1$$
but the result is not 1, it's $$2/a_0^2$$

2. Jun 4, 2012

### Simon Bridge

Don't you need r²dr instead of just dr?
(volume integral, spherical-polar coords.)

3. Jun 4, 2012

### karkas

Yes it appears that solves the problem, thanks!

4. Jun 4, 2012

### karkas

I would enjoy a pointer as to where this comes from exactly, maybe a link?

edit: just standard triple integration in 3 coordinates?

Last edited: Jun 4, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook