Half-line Schrodinger Operators With No Bound States

Details Half-line Schrodinger Operators With No Bound States Half-line Schrodinger Operators With No Bound States

2003-02-28

arxiv.org/abs/math-ph/0303001v1

Physics

Mathematical Physics

34 pages

Scientific paper

We consider Sch\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\Delta + V$ has no spectrum outside of the interval $[-2,2]$, then it has purely absolutely continuous spectrum. In the continuum case we show that if both $-\Delta + V$ and $-\Delta - V$ have no spectrum outside $[0,\infty)$, then both operators are purely absolutely continuous. These results extend to operators with finitely many bound states.

Affiliated with

Also associated with

No associations

Rating

Half-line Schrodinger Operators With No Bound States 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 Half-line Schrodinger Operators With No Bound States, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Half-line Schrodinger Operators With No Bound States will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-66259