2 problems

Let $H_V=H_0+V$ with $V(x,y)=v(x)$, and let the spectral bands be indexed by $n$. Band-width conjecture. The width of each band decreases as $n$ grows, but does not ultimately tend…

Assume Hypothesis … . For each sufficiently small $\epsilon$, let the spectral bands $[a_k,b_k]$ below $E$ be those in Theorem … should remain valid with bands of size … for some…