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

2022/08/18 by Safronov, Oleg
#35P25 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2208.09039

Abstract

For a bounded real-valued function V on \Bbb R^d, we consider two Schrödinger operators H₊=-Δ+V and H_-=-Δ-V. We prove that if the negative spectra H₊ and H_- are discrete and the negative eigenvalues of H₊ and H_- tend to zero sufficiently fast, then the absolutely continuous spectra cover the positive half-line [0,∞).

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