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Complex Extension of Quantum Mechanics
Open accessAbstract
Requiring that a Hamiltonian be Hermitian is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). One might expect a non-Hermitian Hamiltonian to lead to a violation of unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian. Using C, an inner product whose associated norm is positive definite can be constructed. The procedure is general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
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Cited by
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
Self-citationParity–time synthetic photonic lattices
Regensburger, A., Bersch, C., Miri, M.-A., Onishchukov, G., Christodoulides, D. N., & Peschel, U. (2012) · Nature · doi:10.1038/nature11298 · Cited by 2,019
Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control
Deffner, S., & Campbell, S. (2017) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/aa86c6 · Cited by 585
Observation of topological edge states in parity–time-symmetric quantum walks
Xiao, L., Zhan, X., Bian, Z. H., Wang, K. K., Zhang, X., Wang, X. P., Li, J., Mochizuki, K., Kim, D., Kawakami, N., et al. (2017) · Nature Physics · doi:10.1038/nphys4204 · Cited by 576
Biorthogonal quantum mechanics
Brody, D. C. (2014) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/47/3/035305 · Cited by 573
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Metadata
- Authors
- Bender, C. M., Brody, D. C., & Jones, H. F.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-12-16
- Volume
- 89
- Issue
- 27
- Pages
- 270401-270401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2140726841
- Cited by
- 1,839
- References
- 0
- FWCI
- 25.07
- Type
- journal article
- Language
- en
- Open access
- green
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