We consider Schr\"odinger operators with potentials satisfying a generalized bounded variation condition at infinity and an decay condition. This class of potentials includes slowly decaying Wigner--von~Neumann type potentials with . We prove absence of singular continuous spectrum and show that embedded eigenvalues in the continuous spectrum can only take values from an explicit finite set. Conversely, we construct examples where such embedded eigenvalues are present, with exact asymptotics for the corresponding eigensolutions.
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Milivoje Lukic, Schrödinger operators with slowly decaying Wigner–von Neumann type potentials. J. Spectr. Theory 3 (2013), no. 2, pp. 147–169DOI 10.4171/JST/41