# 3D Harmonic Oscillator Circular Orbit

1. Mar 23, 2014

### unscientific

1. The problem statement, all variables and given/known data

I found this in Binney's text, pg 154 where he described the radial probability density $P_{(r)} \propto r^2 u_L$

2. Relevant equations

3. The attempt at a solution

Isn't the radial probability density simply the square of the normalized wavefunction, |ψ(x)|2? Why is there an additional factor of r2?

2. Mar 23, 2014

### BOYLANATOR

When you integrate a function over a volume in spherical co-ordinates you integrate over r2sin(θ)drdθdø . The sin(θ)dθdø goes into the angular function and the r2dr into the radial function. I believe this is where it comes from.

3. Mar 23, 2014

### unscientific

Probability = $<\psi|\psi> = \int \psi^*\psi d^3r = \int \psi^*\psi r^2 dr d\Omega$

Where the wavefunction corresponding to the ket $|\psi>$ is $u_L Y_l^m$

I think that's right.

Last edited: Mar 23, 2014
4. Mar 23, 2014

Correct.