Spherical Multipole Moments - Interior Spherical Multipole Moments

Interior Spherical Multipole Moments

Similarly, the interior multipole expansion has the same functional form

$\Phi(\mathbf{r}) = \frac{1}{4\pi\varepsilon} \sum_{l=0}^{\infty} \sum_{m=-l}^{l} I_{lm} r^{l} \sqrt{\frac{4\pi}{2l+1}} Y_{lm}(\theta, \phi)$

with the interior multipole moments defined as

$I_{lm} \ \stackrel{\mathrm{def}}{=}\ \int d\mathbf{r}^{\prime} \frac{\rho(\mathbf{r}^{\prime})}{\left( r^{\prime} \right)^{l+1}} \sqrt{\frac{4\pi}{2l+1}} Y_{lm}^{*}(\theta^{\prime}, \phi^{\prime})$

Read more about this topic: Spherical Multipole Moments

Famous quotes containing the words interior and/or moments:

“Prose is architecture, not interior decoration, and the Baroque is over.”
—Ernest Hemingway (1899–1961)

“Athletes have studied how to leap and how to survive the leap some of the time and return to the ground. They don’t always do it well. But they are our philosophers of actual moments and the body and soul in them, and of our manoeuvres in our emergencies and longings.”
—Harold Brodkey (b. 1930)