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MxwllsPersuasns
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Homework Statement
Here is a copy of the pdf problem set {https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU} the problem in question is problem number 1 which asks you to prove the orthonormality of the spherical Harmonics Y_1,1 and Y_2,1.
Homework Equations
Y_1,1 = -sqrt(3/8pi)e^(i(/))sin(-)
Y_2,1 = -sqrt(15/8pi)e^(i(/))sin(-)cos(-)
<l,m|l',m'> = Integral from 0 to pi of {sin(-)d(-)}*Integral from 0 to 2pi of {Y*_l,m(Y_l',m')d(/)} = delta_ll'(delta_mm')
(-) = THETA
(/) = PHI
delta = dirac delta function
The Attempt at a Solution
Looking at the 3 equations above something is a little ambiguous. It shows two integrals in the calculation of <l,m|l',m'>, one with d(-) and one with d(/). Now I see that both spehrical harmonics in question have (-) terms, i.e., sin(-), so is that d(-) integral just there from pulling the sin(-) out of Y_1,1 and Y_2,1? That's what I would imagine but it's doesn't explicate a dependence only on (/) in the spherical harmonics (unless the notion of being paired with d(/) only (and not d(-)) is rationale enough to interpret as only being functions of (/))
Actually as I'm looking at the forumlas Y_2,1 couldn't be a function of (/) only after we pulled out the sines as it also has a cos(-) term.. I'm very confused can someone help me move forward here?
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