Must a Hamiltonian be Hermitian
By C. Bender, Dorje C. Brody, H. Jones. 2003
375 citations recorded by the source corpus.
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space–time reflection symmetry (PT symmetry). Thus, there are infinitely many new Hamiltonians that one can construct that might explain experimental data. One would think that a quantum theory based on a non-Hermitian Hamiltonian violates unitarity. However, if PT symmetry is not broken, it is possible to use a previously unnoticed physical symmetry of the Hamiltonian to construct an inner product whose associated norm is positive definite. This construction is general and works for any PT-symmetric Hamiltonian. The dynamics is governed by unitary time evolution. This formulation does not conflict with the requirements of conventional quantum mechanics. There are many possible observable and experimental consequences of extending quantum mechanics into the complex domain, both in particle physics and in solid state physics.
Subfields: Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry
View Paper: https://www.semanticscholar.org/paper/65e37a2af6cd60f5cd90c87b69708e0debe37a22
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In Atomic and Molecular Physics, and Optics
- C. Bender
- Ali Mostafazadeh
- Dorje C. Brody
- Jianke Yang
- Dmitry A. Zezyulin
- Vladimir V. Konotop
- K. Kawabata
- Andrea Alù
In Physical and Theoretical Chemistry
Citations in the corpus
- Observation of PT phase transition in a simple mechanical system (2012, background): “[1–3] The class of PT -symmetric Hamiltonians considered in Refs.”
- Exact PT-symmetry is equivalent to Hermiticity (2003, background): “a Hamiltonian be Hermitian?” posed in the title of [ 17 ]: ‘The Hamiltonian need not be”