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Spherical symmetry

  1. Sep 19, 2012 #1
    I have a problem; I am trying to show the spherical symmetry in a hydrogen atom, for a sum over the l=1 shell i.e the sum over the quadratics over three angular wave equations in l=1,

    |Y10|^2 + |Y11|^2 + |Y1-1.|^2 .

    This should equal up to a constant or a zero to yield no angular dependence. m goes from -l to l.



    The problem is that when trying to do this, i get all kinds o different sin, cos formulas, which i cannot reduce to zero or a constant to make the total equation only radial dependent - or am i doing this the wrong way?


    Anyone who did this problem?
     
    Last edited: Sep 19, 2012
  2. jcsd
  3. Sep 19, 2012 #2

    gabbagabbahey

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    It sounds like you have the correct approach. Why don't you show us your calculation so we can tell you where you are going wrong.
     
  4. Sep 19, 2012 #3
    I have: [tex]|\frac{1}{2}\sqrt{3/2\pi}\sin\theta e^{-i\delta}|^2+|\frac{1}{2}\sqrt{3/2\pi}\sin\theta e^{i\delta}|^2 + |\frac{1}{2}\sqrt{3/\pi}\cos\theta|^2[/tex]

    which i finally got to: [tex]\frac{3}{4\pi}((\cos\theta)^2 + (\sin\theta)^2((\cos\delta)^2 - (\sin\delta)^2)[/tex]

    which i obviously cannot get to a constant or zero.
     
  5. Sep 19, 2012 #4

    gabbagabbahey

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    The deltas should disappear when you take the modulus of each term. For a complex number, the modulus is defined as [itex]|z|=\sqrt{zz^*}[/itex], you don't just square the number, you multiply by its complex-conjugate.
     
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