Controllability of pure states for the Pöschl-Teller potential with a dynamical group SU(2)

The controllability of a quantum system for the modified Pöschl-Teller (MPT) potential with the discrete bound states is investigated. The creation and annihilation operators of this potential are constructed directly from the normalized wave function with the factorization method and associated to an su(2) algebra. It is shown that this quantum system with the nondegenerate discrete bound states can, in principle, be strongly completely controllable, i.e., the system eigenstates can be guided by the external field to approach arbitrarily close to a target state, which could be theoretically realized by the actions of the creation and annihilation operators on the ground state.