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On the invariant method for the time-dependent non-Hermitian Hamiltonians

  • B. Khantoul
  • A. Bounames
  • M. Maamache
Regular Article

Abstract.

We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators H(t) that generate a real phase in their time evolution. This involves the use of invariant operators \( I_{PH}(t)\) that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore, H(t) is generally not quasi-Hermitian and does not define an observable of the system but \( I_{PH}(t)\) obeys a quasi-Hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Theoretical Physics Laboratory, Department of PhysicsUniversity of JijelJijelAlgeria
  2. 2.Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des SciencesUniversité Ferhat Abbas Sétif 1SétifAlgeria

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