Absolutely continuous spectrum of a typical Schr\"odinger operator with   a slowly decaying potential
  We consider a family of multi-dimensional Schr\"odinger operators $-\Delta+t V$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the absolutely continuous spectrum of this operator covers the interval $[0,\infty)$ for almost every $t$. 
Oleg Safronov
math-ph math.MP math.SP