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Angle in Spherical coordinates

  1. Apr 17, 2009 #1

    Matterwave

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    Gold Member

    I have to proove something in QM but I'm stuck on a bit of math.

    Say I have two vectors:

    [tex]\vec{a} = (r_a,\theta_a,\phi_a)[/tex]
    and
    [tex]\vec{b} = (r_b,\theta_b,\phi_b)[/tex]

    What is the cosine of the angle between them? If my proof is to work the cosine of the angle between them have to be:

    [tex]cos(\theta)=1+sin(\theta_a)sin(\theta_b)cos(\phi_a-\phi_b)[/tex]

    I think the 1 is erroneous and should be replaced with
    [tex]cos(\theta_a)cos(\theta_b)[/tex]
    But I'm not sure and I can't figure out what I did wrong...Which one is it? Is it either?
     
  2. jcsd
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