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Two-body threshold spectral analysis, the critical case

Publikation: Working paper/Preprint Working paperForskning

  • Institut for Matematiske Fag
We study in dimension $d\geq2$ low-energy spectral and scattering asymptotics for two-body $d$-dimensional Schrödinger operators with a radially symmetric potential falling off like $-\gamma r^{-2},\;\gamma>0$. We consider angular momentum sectors, labelled by $l=0,1,\dots$, for which $\gamma>(l+d/2 -1)^2$. 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.
UdgiverAarhus University, Department of Mathematical Sciences
Antal sider25
StatusUdgivet - 2010

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