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Non-Hermitian Quantum Mechanics
Abstract
Non-Hermitian quantum mechanics (NHQM) is an important alternative to the standard (Hermitian) formalism of quantum mechanics, enabling the solution of otherwise difficult problems. The first book to present this theory, it is useful to advanced graduate students and researchers in physics, chemistry and engineering. NHQM provides powerful numerical and analytical tools for the study of resonance phenomena - perhaps one of the most striking events in nature. It is especially useful for problems whose solutions cause extreme difficulties within the structure of a conventional Hermitian framework. NHQM has applications in a variety of fields, including optics, where the refractive index is complex; quantum field theory, where the parity-time (PT) symmetry properties of the Hamiltonian are investigated; and atomic and molecular physics and electrical engineering, where complex potentials are introduced to simplify numerical calculations.
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“The concept of biorthonormal basis [44, 45] plays an important role in non-Hermitian quantum mechanics.”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [44]
In the citing paper
“In addition, the fact that 〈 〈 ξ k | is orthogornal to | ζ k ′ 〉 〉 , (199), even though the two sets {〈 〈 ξ k | } and {| ζ k 〉 〉} are not conjugate transpose of each other, implies that the superoperators {| ζ k 〉 〉〈 〈 ξ k | } constitute what we call a biorthonormal basis [44, 45] for S d .”
From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [44]
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Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D., & Marin Soljacic, A. (2016) · Nature Reviews Materials · doi:10.1038/natrevmats.2016.48 · Cited by 3,483
Non-Hermitian physics and PT symmetry
El‐Ganainy, R., Makris, K. G., Khajavikhan, M., Musslimani, Z. H., Rotter, S., & Christodoulides, D. N. (2018) · Nature Physics · doi:10.1038/nphys4323 · Cited by 2,767
Exceptional points in optics and photonics
Miri, M., & Alù, A. (2019) · Science · doi:10.1126/science.aar7709 · Cited by 2,270
Enhanced sensitivity at higher-order exceptional points
Hodaei, H., Hassan, A. U., Wittek, S., Garcia-Gracia, H., El‐Ganainy, R., Christodoulides, D. N., & Khajavikhan, M. (2017) · Nature · doi:10.1038/nature23280 · Cited by 1,860
Non-Hermitian photonics based on parity–time symmetry
Feng, L., El‐Ganainy, R., & Ge, L. (2017) · Nature Photonics · doi:10.1038/s41566-017-0031-1 · Cited by 1,501
Metadata
- Authors
- Moiseyev, N.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Corresponding author
- Moiseyev, Nimrod
- ORCID
- Moiseyev, Nimrod
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2011-02-17
- OpenAlex
- W1649271673
- Cited by
- 1,490
- References
- 0
- Citations by year
- 2026: 77 · 2025: 109 · 2024: 100 · 2023: 104 · 2022: 139 · 2021: 111 · 2020: 154 · 2019: 153 · 2018: 116 · 2017: 101 · 2016: 77 · 2015: 80 · 2014: 48 · 2013: 63 · 2012: 34
- FWCI
- 12.63
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- non-Hermitian quantum mechanics, complex potentials, resonance, PT symmetry, PT-symmetric Hamiltonians, complex refractive index, complex Hamiltonian, non-Hermitian photonics, quantum field theory, atomic and molecular physics
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