Journal of Mathematical Physics

The pseudo Hermitian invariant operator and time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry

Walid Koussa, Naima Mana, Oum Kaltoum Djeghiour, Mustapha Maamache

Published Jul 1, 2018• 18 citations

Abstract

We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry. With a time-dependent metric, the pseudo-Hermitian invariant operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the pseudo-Hermitian invariant operator. Finally some interesting physical applications are suggested and discussed.

DOI: 10.1063/1.5041718

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