PT-symmetry and Schrödinger operators. The double well case

DOI10.1002/mana.201500075zbMath1337.35103arXiv1502.06102OpenAlexW2964034267MaRDI QIDQ2808131

Johannes Sjöstrand, Naima Boussekkine, Nawal Mecherout, Thierry Ramond

Publication date: 26 May 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.06102

zbMATH Keywords

eigenvaluesSchrödinger operators\(\mathcal{PT}\)-symmetrycomplex WKB analysisquantization conditon

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) PDEs in connection with quantum mechanics (35Q40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (4)

Real eigenvalues of a non-self-adjoint perturbation of the self-adjoint Zakharov-Shabat operator ⋮ Non-real eigenvalues for \(\mathcal{PT}\)-symmetric double wells ⋮ Complex eigenvalue splitting for the Dirac operator ⋮ PT-symmetry and potentiel well. The simple well case

Uses Software

• Matplotlib

Cites Work

• Unnamed Item
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• Perturbation theory of symmetric Hamiltonians
• symmetric non-self-adjoint operators, diagonalizable and non-diagonalizable, with a real discrete spectrum
• Supersymmetry without Hermiticity within \(\mathcal{PT}\) symmetric quantum mechanics

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