Octupole Expansion

I have used a whole month to do this derivation.

$\displaystyle{V(\mathbf{R}) = ... + \frac{1}{4 \pi \varepsilon_0} \frac{3}{2 |\mathbf R|^4} \sum_{ijk} \hat R_i \hat R_j \hat R_k Q_{ijk} + ... }$

$\displaystyle{Q_{ijk} = \int_{\mathbf r} \left[ \delta_{ij} ( r^2 - 5 r_i r_j + \frac{10}{3} r_i r_j \delta_{jk} ) r_k - |\epsilon_{ijk}| 10 r_i r_j r_k \right] \rho(\mathbf r) d^3 r}$

But I still do not know whether it is correct or not.

Physics Town

continues

Octupole Expansion

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