Asymptotics of spectral gaps of the 1D schrodinger operator with Mathieu potential

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Anahtarcı, Berkay (2011) Asymptotics of spectral gaps of the 1D schrodinger operator with Mathieu potential. [Thesis]

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Abstract

The one-dimensional Schrödinger operator L(y) = -yn + v(x)y, considered on R with π[pi]-periodic real-valued potential v(x), is self-adjoint, and its spectrum has a gap-band structure- the intervals of continuous spectrum are separated by spectral gaps. In this thesis, we study the asymptotic behaviour of the spectral gaps of L. In the case of the Mathieu potential v(x) = 2a cos (2x), we give an alternative proof of the result of Harrell-Avron-Simon about the precise asymptotics of the lengths of spectral gaps.
Item Type: Thesis
Uncontrolled Keywords: Floquet theory. -- Stability zones. -- Projection method (Lyapunov-Schmidt). -- Mathieu potantial. -- Floquet teorisi. -- Stabilite bölgeleri. -- İzdüşüm yöntemi (Lyapunov-Schmidt). -- Mathieu potansiyeli.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: IC-Cataloging
Date Deposited: 28 Jun 2013 15:03
Last Modified: 26 Apr 2022 09:58
URI: https://research.sabanciuniv.edu/id/eprint/21645

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