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: Finding Quantum numbers from wavefunction

  1. Nov 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider a spinless particle in a central field in a state described by:
    [tex] \psi_a(r) = (x^2 - y^2) e^{-\alpha r^2} [/tex]
    [tex] \psi_b(r) = xyz e^{-\alpha r^2} [/tex]

    Find quantum numbers [tex] l [/tex] and [tex] l_z [/tex] (or their appropriate superposition) for these two cases.

    2. Relevant equations

    [tex] \psi(r) = \psi(r, \theta, \phi) = R(r)Y(\theta, \phi) [/tex]

    3. The attempt at a solution

    Okay so I am not sure where to start with this problem, I could construct the Schrodinger equation in terms of the radial and spherical harmonics and then we know that [tex] l [/tex] can be determined from this equation, yet I do not know what the potential for such equation should be.
  2. jcsd
  3. Nov 25, 2013 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You don't need to use the Schrodinger equation. Express the wave functions in spherical coordinates and separate it into an angular part and a radial part. You want to express the angular part as a linear combination of the spherical harmonics.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted