1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 3D Harmonic Oscillator Circular Orbit

  1. Mar 23, 2014 #1
    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. jcsd
  3. Mar 23, 2014 #2
    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.
  4. Mar 23, 2014 #3

    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
  5. Mar 23, 2014 #4
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted