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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

    vela

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    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.
     
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