Must a Hamiltonian be Hermitian

@article{Bender2003MustAH,
  title={Must a Hamiltonian be Hermitian},
  author={Carl M Bender and Dorje C. Brody and H F Jones},
  journal={American Journal of Physics},
  year={2003},
  volume={71},
  pages={1095-1102}
}
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… 

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