Transition elements for a non-Hermitian quadratic Hamiltonian

DOI10.1063/1.1640796zbMath1070.81053OpenAlexW2064821571MaRDI QIDQ4833312

Mark S. Swanson

Publication date: 15 December 2004

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

Full work available at URL: https://doi.org/10.1063/1.1640796

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

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Cites Work

• Complex Extension of Quantum Mechanics
• All Hermitian Hamiltonians have parity
• 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
• Space of state vectors in 𝒫𝒯-symmetric quantum mechanics
• 𝓟𝓣-symmetric quantum mechanics
• Quantum complex Hénon-Heiles potentials