Schr\"odinger operators periodic in octants

Evgeny Korotyaev; Jacob Schach Moller

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arXiv · 1712.08893

Schr\"odinger operators periodic in octants

Evgeny Korotyaev·Jacob Schach Moller

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Abstract

We consider Schr\"odinger operators with periodic potentials in the positive quadrant for dim $>1$ with Dirichlet boundary condition. We show that for any integer $N$ and any interval $I$ there exists a periodic potential such that the Schr\"odinger operator has $N$ eigenvalues counted with the multiplicity on this interval and there is no other spectrum on the interval. Furthermore, to the right and to the left of it there is a essential spectrum. Moreover, we prove similar results for Schr\"odinger operators for other domains. The proof is based on the inverse spectral theory for Hill operators on the real line.

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BibTeX RIS

Evgeny Korotyaev, Jacob Schach Moller. 2017-12-24. Schr\"odinger operators periodic in octants. https://arxiv.org/abs/1712.08893

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