Aarhus Universitets segl

English

Du er her: AU » Om AU » Organisation » Two-body threshold spectral analysis, the critical case

Om AU

Two-body threshold spectral analysis, the critical case

Publikation: Working paper/Preprint › Working paper › Forskning

Links

  • 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.
OriginalsprogEngelsk
UdgivelsesstedÅrhus
UdgiverAarhus University, Department of Mathematical Sciences
Antal sider25
StatusUdgivet - 2010

Se relationer på Aarhus Universitet Citationsformater

ID: 34321649