Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591156 | Journal of Functional Analysis | 2011 | 29 Pages |
Abstract
We study in dimension d⩾2 low-energy spectral and scattering asymptotics for two-body d-dimensional Schrödinger operators with a radially symmetric potential falling off like −γr−2, γ>0. We consider angular momentum sectors, labelled by l=0,1,…, for which γ>2(l+d/2−1). In each such sector the reduced Schrödinger operator has infinitely many negative eigenvalues accumulating at zero. We show that the resolvent has a non-trivial oscillatory behaviour as the spectral parameter approaches zero in cones bounded away from the negative half-axis, and we derive an asymptotic formula for the phase shift.
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