- #1

## Homework Statement

Show that the (1,0,0) and (2,0,0) wave functions are properly normalized.

We know that:

Ψ(1,0,0) = (2/(a0^(3/2))*e^(-r/a0)*(1/sqrt(2))*(1/sqrt(2*pi))

where:

R(r) = (2/(a0^(3/2))*e^(-r/a0)

Θ(θ) = (1/sqrt(2))

Φ(φ) = (1/sqrt(2*pi))

## Homework Equations

(1) ∫|Ψ|^2 dx = 1

(2) |R(r)|^2*|Θ(θ)|^2*|Φ(φ)|^2*r^2*sinθ dr dθ dφ ... (? might be useful)

## The Attempt at a Solution

So I know that in order for a function to be properly normalized, it has to have the absolute value of the sine wave squared equal to 1. I originally integrated from negative inf to positive inf, but that did not give me 1 = 1. I tried looking to see where I went wrong but I found equation (2) in my book, but wasn't sure how to integrate that. What am I doing wrong? I think my limits of integration might be wrong because I was doing:

(3) ∫ ((2/(a0^(3/2))*e^(-r/a0)*(1/sqrt(2))*(1/sqrt(2*pi)))^2 dr = 1 from - inf to + inf

and not worrying about that sin θ thing I mentioned earlier.

Do I need to be using equation (2)? How do I find limits of integration? I know that - infinity doesn't make sense for r, so maybe it is just from 0 to infinity with equation 3 maybe?