Non-Hermitian Hamiltonians, Metric, Other Observables and Physical Implications

Details Non-Hermitian Hamiltonians, Metric, Other Observables and Physical Implications Non-Hermitian Hamiltonians, Metric, Other Observables and Physical Implications

2007-10-30

arxiv.org/abs/0710.5593v1

Physics

Quantum Physics

submitted for publication in J Phys A, special issue PHHQM07

Scientific paper

The metric associated with a quasi-Hermitian Hamiltonian and its physical implications are scrutinised. Consequences of the non-uniqueness such as the question of the probability interpretation and the possible and forbidden choices of additional observables are investigated and exemplified by specific illustrative examples. In particular it is argued that the improper identification of observables lies at the origin of the claimed violation of the brachistchrone transition time between orthogonal states. The need for further physical input to remove ambiguities is pointed out.

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