Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations

Details Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations

2011-12-20

arxiv.org/abs/1112.4717v2

Mathematics

Spectral Theory

18 pages, 1 figure

Scientific paper

The spectrum of the self-adjoint Schroedinger operator associated with the Kronig-Penney model on the half-line has a band-gap structure: its absolutely continuous spectrum consists of intervals (bands) separated by gaps. We show that if one changes strengths of interactions or locations of interaction centers by adding an oscillating and slowly decaying sequence which resembles the classical Wigner-von Neumann potential, then this structure of the absolutely continuous spectrum is preserved. At the same time in each spectral band precisely two critical points appear. At these points "instable" embedded eigenvalues may exist. We obtain locations of the critical points and discuss for each of them the possibility of an embedded eigenvalue to appear. We also show that the spectrum in gaps remains pure point.

Affiliated with

Also associated with

No associations

Rating

Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations 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 Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral analysis of the Kronig-Penney model with Wigner-von Neumann perturbations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-58337