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May 2006 Spectral gaps of the one-dimensional Schr\"odinger operators with periodic point interactions
Kazushi YOSHITOMI
Hokkaido Math. J. 35(2): 365-378 (May 2006). DOI: 10.14492/hokmj/1285766361

Abstract

We study the spectral gaps of the Schr{\"o}dinger operators $$H_{1}=-\frac{d^{2}}{dx^{2}}+\sum^{\infty}_{l=-\infty}( \beta_{1}\delta^{\prime}(x-\kappa-2\pi l)+\beta_{2}\delta^{\prime}(x-2\pi l))\quad {\rm in}\quad L^{2}({\mathbb R}),$$ $$H_{2}=-\frac{d^{2}}{dx^{2}}+\sum^{\infty}_{l=-\infty}( \beta_{1}\delta(x-\kappa-2\pi l)+\beta_{2}\delta(x-2\pi l))\quad {\rm in}\quad L^{2}({\mathbb R}),$$ where $\kappa\in (0,2\pi)$ and $\beta_{1},\beta_{2}\in{\mathbb R}\backslash\{0\}$ are parameters. Given $j\in{\mathbb N}$, we determine whether the $j$th gap of $H_{k}$ is absent or not for $k=1,2$.

Citation

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Kazushi YOSHITOMI. "Spectral gaps of the one-dimensional Schr\"odinger operators with periodic point interactions." Hokkaido Math. J. 35 (2) 365 - 378, May 2006. https://doi.org/10.14492/hokmj/1285766361

Information

Published: May 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1114.34067
MathSciNet: MR2254656
Digital Object Identifier: 10.14492/hokmj/1285766361

Subjects:
Primary: 34B37
Secondary: 34B30, 34D08, 34L40

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 2 • May 2006
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