Exactly solvable time-dependent non-Hermitian quantum systems from point transformations

We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for quantum systems. Initially we identify a transformation as map from an exactly solvable time-independent system explicitly Hamiltonian system. Subsequently employ the invariant latter Exploiting fact this is pseudo-Hermitian, corresponding adjoint action Hermitian invariant, thus obtaining solutions quasi-Hermiticity equation together with Schrödinger equation.