Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators

Details Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators

2004-06-24

arxiv.org/abs/math/0406491v2

Mathematics

Spectral Theory

27 pages, 15 figures

Scientific paper

We study the behavior of the limit of the spectrum of a non self-adjoint Sturm-Liouville operator with analytic potential as the semi-classical parameter $h\to 0$. We get a good description of the spectrum and limit spectrum near $\infty$. We also study the action of one special perturbation of the operator (adding a Heaviside function), and prove that the limit spectrum is very unstable. As an illustration we describe the limit spectrum as $h\to 0$ for $P^h=-h^2\Delta+i x^2$ and the effect of this perturbation.

Affiliated with

Also associated with

No associations

Rating

Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators 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 Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101857