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We study the time evolution of quantum systems with a time-dependentnon-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2)generators.With a time-dependent metric, the pseudo-Hermitian invariantoperator is constructed in the same manner as for both the SU(1,1) and SU(2)systems. The exact common solutions of the Schr\"odinger equations for both theSU(1,1) and SU(2) systems are obtained in terms of eigenstates of thepseudo-Hermitian invariant operator.

Time evolution of quantum systems with time-dependent non-Hermitian Hamiltonian and the pseudo Hermitian invariant operator