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Discrete Spectrum of a Periodic Schrödinger Operator Perturbed by a Rapidly Decaying Potential

Abstract

Let \([\lambda ,\mu ]\) be an interval contained in a spectral gap of a periodic Schrödinger operator H. Consider \(H(\alpha )=H-\alpha V\) where V is a fast decaying positive function. We study the asymptotic behavior of the number of eigenvalues of \(H(\alpha )\) in \([\lambda ,\mu ]\) as \(\alpha \rightarrow \infty \).

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Correspondence to Oleg Safronov.

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Communicated by Jan Derezinski.

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Safronov, O. Discrete Spectrum of a Periodic Schrödinger Operator Perturbed by a Rapidly Decaying Potential. Ann. Henri Poincaré 23, 1883–1907 (2022). https://doi.org/10.1007/s00023-021-01141-1

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  • DOI: https://doi.org/10.1007/s00023-021-01141-1

Mathematics Subject Classification

  • 81Q10 (35P20)