Two-body threshold spectral analysis, the critical case

Details Two-body threshold spectral analysis, the critical case Two-body threshold spectral analysis, the critical case

2010-06-14

arxiv.org/abs/1006.2676v1

Mathematics

Spectral Theory

Scientific paper

We study in dimension $d\geq2$ low-energy spectral and scattering asymptotics for two-body $d$-dimensional Schr\"odinger 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 Schr\"odinger 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.

Affiliated with

Also associated with

No associations

Rating

Two-body threshold spectral analysis, the critical case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Two-body threshold spectral analysis, the critical case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two-body threshold spectral analysis, the critical case will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422288