Article ID Journal Published Year Pages File Type
1900387 Reports on Mathematical Physics 2014 28 Pages PDF
Abstract

The spectrum of the self-adjoint Schrödinger 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 discrete.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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