On the controllability of a quantum system for the Morse potential with a compact group SU(2)

The controllability of a quantum system for the Morse potential with the bound states are investigated. The ladder operators are constructed directly from the wave functions with the factorization method and associated to an su(2) algebra. This quantum system with the discrete bound states can be strongly completely controlled, i.e., the eigenstates can be guided by the external field to approach arbitrarily close to a selected target state at any chosen time, which can be theoretically realized by the actions of the ladder operators on the ground state