https://doi.org/10.1140/epjp/i2017-11678-2
Regular Article
Pseudo-invariants theory and real phases for systems with non-Hermitian time-dependent Hamiltonians
1
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
* e-mail: maamache@univ-setif.dz
Received:
9
May
2017
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
