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I am interested in the following question. So let suppose we have finite number of point particles on plane $\mathbb{R}^2$. We can assume that every $j$ point is represented by Dirac delta function $\...

Let \begin{equation*} V(x) = -\big(2-\sin(2\pi x) - \sin(2\pi \sqrt{2}x)\big)^\gamma \end{equation*} for some $\gamma \in (0,1]$. Define for each $r<0$ the number $$a_r = \min\{a>0: V(a) = ...