Pseudo-invariants theory and real phases for systems with non-Hermitian time-dependent Hamiltonians
Laboratoire de Physique Quantique et Systèmes Dynamiques, Faculté des Sciences, Université Ferhat Abbas Sétif 1, 19000, Sétif, Algeria
2 Département de Physique, Université de Jijel, BP 98 Ouled Aissa, 18000, Jijel, Algeria
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Accepted: 2 August 2017
Published online: 8 September 2017
In this paper, the Lewis-Riesenfeld invariant theory is generalized for the study of systems with non-Hermitian time-dependent Hamiltonians. Explicitly time-dependent pseudo-Hermitian invariants theory, with a time-dependent metric, is developed. We derive a simple relation between the eigenstates of this pseudo-Hermitian invariant and the solutions of the Schrödinger equation. A physical system is treated in detail: the time-dependent Swanson model, where an explicitly time-dependent pseudo-Hermitian invariant is derived as well as their eigenvalues and eigenstates.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, 2017