A criterion for the reality of the spectrum of \(PT\)-symmetric Schrödinger operators with complex-valued periodic potentials

DOI10.4171/RLM/515zbMath1229.34128arXiv0804.4578OpenAlexW2963079669MaRDI QIDQ658523

Sandro Graffi, Emanuela Caliceti

Publication date: 12 January 2012

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.4578

zbMATH Keywords

real spectrum\(PT\)-symmetryperiodic potentials

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (3)

Non-real eigenvalues for \(\mathcal{PT}\)-symmetric double wells ⋮ PT-symmetry and potentiel well. The simple well case ⋮ PT-symmetry and Schrödinger operators. The double well case

Cites Work

• Unnamed Item
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• Schrödinger operators with complex potential but real spectrum
• Complex periodic potentials with real band spectra.
• Generalized PT symmetry and real spectra
• 𝓟𝓣-symmetric quantum mechanics
• Energy band structure due to a complex, periodic, PT-invariant potential

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