Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

Fring, A. ORCID: 0000-0002-7896-7161 & Frith, T. (2018). Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians. Physics Letters A, doi: 10.1016/j.physleta.2018.10.043

Abstract

For a large class of time-dependent non-Hermitian Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the time-dependent Dyson equation. A specific Hermitian model with explicit time-dependence is analyzed further and shown to be quasi-exactly solvable. Technically we constructed the Lewis–Riesenfeld invariants making use of the metric picture, which is an equivalent alternative to the Schrödinger, Heisenberg and interaction picture containing the time-dependence in the metric operator that relates the time-dependent Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.

Publication Type:	Article
Additional Information:	© 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords:	Time-dependent Schrödinger equation, Quasi-exactly solvable models, Non-Hermitian quantum mechanics, PT-symmetry, Lewis–Riesenfeld invariants
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics