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For a bounded real-valued function $V$ on ${\Bbb R}^d$, we consider twoSchr\"odinger operators $H_+=-\Delta+V$ and $H_-=-\Delta-V$. We prove that ifthe negative spectra $H_+$ and $H_-$ are discrete and the negative eigenvaluesof $H_+$ and $H_-$ tend to zero sufficiently fast, then  the absolutely continuous spectra cover the positive half-line $[0,\infty)$.

The rate of accumulation of negative eigenvalues to zero and the absolutely continuous spectrum