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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?
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?