- #1
QMrocks
- 85
- 0
Happy New Year all!
i have a question regarding the addition theorem for spherical harmonics. In JD Jackson book pg 110 for e.g. the addition theorem is given as:
[tex]
P_{L}(cos(\gamma))=\frac{4\pi}{2L+1}\sum_{m=-L}^{L}Y^{*}_{Lm}(\theta',\phi')Y_{Lm}(\theta,\phi)
[/tex]
where [tex] cos(\gamma)=cos\theta cos\theta' + sin\theta sin\theta' cos(\phi-\phi') [/tex]. The 2 coordinate system[tex] (r,\theta,\phi) [/tex]and[tex] (r',\theta',\phi')[/tex] have an angle [tex]\gamma [/tex] between them.
My question is:
How can we express [tex]Y_{Lm}(\theta',\phi') [/tex] in terms of [tex]Y_{Lm}(\theta,\phi) [/tex] ?
i have a question regarding the addition theorem for spherical harmonics. In JD Jackson book pg 110 for e.g. the addition theorem is given as:
[tex]
P_{L}(cos(\gamma))=\frac{4\pi}{2L+1}\sum_{m=-L}^{L}Y^{*}_{Lm}(\theta',\phi')Y_{Lm}(\theta,\phi)
[/tex]
where [tex] cos(\gamma)=cos\theta cos\theta' + sin\theta sin\theta' cos(\phi-\phi') [/tex]. The 2 coordinate system[tex] (r,\theta,\phi) [/tex]and[tex] (r',\theta',\phi')[/tex] have an angle [tex]\gamma [/tex] between them.
My question is:
How can we express [tex]Y_{Lm}(\theta',\phi') [/tex] in terms of [tex]Y_{Lm}(\theta,\phi) [/tex] ?