Yes!
with the ansatz in the equation of motion, i obtain
\mathcal{A}=\frac{3}{2m}\sum_{i\neq j}\left[1-\frac{5}{|\vec{r}_i^0-\vec{r}_j^0|^2}\left(\vec{r}_i^0-\vec{r}_j^0\right)^2 \right]\frac{\left(1-e^{i\vec{q}(\vec{r}_i^0-\vec{r}_j^0)}\right)}{|\vec{r}_i^0-\vec{r}_j^0|^5}
What I...
Hello,
I want to prove that the function \mathcal{A} in the 1D case satisfy
\mathcal{A}=\frac{48}{m}\sum_{j=1}^\infty \frac{\sin^2(qj/2)}{j^5}=\frac{12}{m}\left[2\zeta(5)-\text{Li}_5(e^{iq})-\text{Li}_5(e^{-iq})\right],
with \text{Li}_n(z) the polylogarithm function, and the matrix...