On the theory of \(\mathcal{PT}\)-symmetric operators

DOI10.1007/S11253-012-0628-YzbMath1275.47085OpenAlexW2079006969MaRDI QIDQ1933310

O. M. Patsyuk, Sergei Kuzhel

Publication date: 23 January 2013

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-012-0628-y

zbMATH Keywords

Krein spaces\(\mathcal{PT}\)-symmetric operatorsnon-selfadjoint Hamiltonians

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Linear operators on spaces with an indefinite metric (47B50) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (1)

Conjugations on \(L^2\) space on the real line

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Extension theory for symmetric operators and boundary value problems for differential equations
• \(PT\) symmetric Schrödinger operators: reality of the perturbed eigenvalues
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• On a class of \(J\)-self-adjoint operators with empty resolvent set
• Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
• On self-adjoint operators in Krein spaces constructed by Clifford algebra Cl_2
• \mathcal {P}\mathcal {T}-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Bakerian Lecture - The physical interpretation of quantum mechanics

This page was built for publication: On the theory of \(\mathcal{PT}\)-symmetric operators