On absolute continuity of the periodic Schrödinger operators (Q2708372)

Let \(W\) be a real periodic function on \(\mathbb{R}^d\), that is \(W(x +e_j) =W(x)\), \(j=1,\dots,d\), for some basis \(\{e_j\}^d_{j=1}\) of \(\mathbb{R}^d\). The author is interested in the spectral properties of the periodic Schrödinger operator \(-\Delta+W(x)\) in \(\mathbb{R}^d\). In particular he proves that the spectrum \(-\Delta+ W(x)\) is purely absolutely continuous, if \(d\geq 3\) and \(W\in L^{d/2}_{ \text{loc}}(\mathbb{R}^d)\).