\(PT\) symmetric Schrödinger operators: reality of the perturbed eigenvalues

DOI10.3842/SIGMA.2010.009zbMath1202.47014arXiv1001.3656OpenAlexW2137688545MaRDI QIDQ970315

Sandro Graffi, Emanuela Caliceti, Francesco Cannata

Publication date: 17 May 2010

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3656

zbMATH Keywords

perturbation theoryPT symmetryreal spectraperturbed eigenvaluesSchrödinger operators family

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Perturbation theory of linear operators (47A55) Eigenvalue problems for linear operators (47A75) Schrödinger operator, Schrödinger equation (35J10) Perturbation theories for operators and differential equations in quantum theory (81Q15)

Related Items (7)

On the theory of \(\mathcal{PT}\)-symmetric operators ⋮ Eigensystem of an \(L ^{2}\)-perturbed harmonic oscillator is an unconditional basis ⋮ A Hamiltonian formulation of the Pais-Uhlenbeck oscillator that yields a stable and unitary quantum system ⋮ Boundary-value problems for the evolutionary Schrödinger equation. I ⋮ Anharmonic oscillators in the complex plane, \(\mathcal{PT}\)-symmetry, and real eigenvalues ⋮ Three PT-symmetric Hamiltonians with completely different spectra ⋮ Spectra of $\mathcal{PT}$-symmetric operators under rank-one perturbations

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