I'm doing Griffith Problem 5.11 and I'm stuck on how to do the integration. My prof. gave hints on how to simplify the integration with the following formula:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{1}{|{\vec r}_{1}-{\vec r}_{2}|} = \sum_{\ell = 0}^{\infty}

P_{\ell}( \cos \theta) \frac{r_{<}^{\ell}}{r_{>}^{\ell +1}}[/tex]

where

[tex]\cos \theta = \frac{{\vec r}_1 \cdot {\vec r}_2}{r_1 r_2}[/tex]

[tex]P_{\ell}(x)=\frac{1}{2^{\ell}\ell !}(\frac{d}{dx})^{\ell}(x^{2}-1)^{\ell}[/tex]

[tex]r_<[/tex] is the smaller of [tex]|{\vec r}_1|, |{\vec r_2}|[/tex]

I haven't had advanced electrodynamics yet so it's my first time seeing this type of expansion.

Since I don't really know if [tex]\vec r}_1[/tex] is bigger or smaller than [tex]\vec r}_2[/tex], do I need to do expansion for both cases and add them?...

How many terms do I keep in Legendre polynomial? I recall professor saying something about only one or two terms, but I don't see how you can truncate the series like that...

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# Quantum Mechanics Integration Problem

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