On the Schrödinger operator with a periodic PT-symmetric matrix potential

DOI10.1063/5.0064516zbMath1492.34087arXiv2107.10736OpenAlexW3202620759MaRDI QIDQ5163834

Oktay A. Veliev

Publication date: 8 November 2021

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.10736

zbMATH Keywords

Schrödinger equation, PT-symmetric periodic matrix potential

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Cites Work

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• \({\mathcal{PT}}\)-symmetric periodic optical potentials
• Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients
• On non-self-adjoint Sturm-Liouville operators with matrix potentials
• Operators commuting with translation by one. II: Differential operators with periodic coefficients in \(L_ p(-\infty,\infty)\)
• On Hill's operator with a matrix potential
• On the shape of spectra for non-self-adjoint periodic Schrödinger operators
• Non-self-adjoint Schrödinger Operator with a Periodic Potential

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