Hybrid form of quantum theory with non-Hermitian Hamiltonians

DOI10.1016/j.physleta.2022.128556OpenAlexW4309574794MaRDI QIDQ2111363

Miloslav Znojil

Publication date: 13 January 2023

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.10633

zbMATH Keywords

factorized Dyson mapHermitization using a combined amendment of the inner product and Hamiltonianhiddenly Hermitian quantum Hamiltoniansnon-Hermitian quantum mechanics of unitary systems

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Schrödinger operator, Schrödinger equation (35J10) Factorization systems, substructures, quotient structures, congruences, amalgams (18A32) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (1)

Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation

Uses Software

• Maple
• Eigtool

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Investigation of non-Hermitian Hamiltonians in the Heisenberg picture
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Three-Hilbert-space formulation of quantum mechanics
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Non-Hermitian Heisenberg representation
• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
• Non-Selfadjoint Operators in Quantum Physics
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• General Theory of Spin-Wave Interactions
• Equivalence of unstable anharmonic oscillators and double wells
• 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
• The minimally anisotropic metric operator in quasi-Hermitian quantum mechanics
• Pseudo-Hermiticity and generalized PT- and CPT-symmetries

This page was built for publication: Hybrid form of quantum theory with non-Hermitian Hamiltonians