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 plays an important role in non-Hermitian quantum mechanics.
“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]
The superoperators {|ζ_k〉〈ξ_k|} constitute a biorthonormal basis for S_d.
“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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- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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