For a large class of multi-dimensional Schrödinger operators it is shown that the absolutely continuous spectrum is essentially supported by [0, ∞). We require slow decay and mildly oscillatory behavior of the potential in a cone and can allow for arbitrary non-negative bounded potential outside the cone. In particular, we do not require the existence of… (More)
acting in the space L 2 (R d). We study the relation between the behavior of V at the infinity and the properties of the negative spectrum of H. According to the Cwikel-Lieb-Rozenblum estimate , , the number of negative eigenvalues of H satisfies the relation (1.1) N ≤ C V d/2 dx, d ≥ 3, where C is independent of V. Similar estimates hold in… (More)
We study the distribution of eigenvalues of the Schrödinger operator with a complex valued potential V. We prove that if |V | decays faster than the Coulomb potential, then all eigenvalues are in a disc of a finite radius.
We study the eigenvalues of Schrödinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.