| A problem of controllability for time-dependent quantum control systems is posed. Because operators involved in such systems acting on infinite-dimensional Hilbert spaces are unbounded in general, we introduce analytic domains which are dense and invariant under the actions both of these operators and of the exponentiations of these operators. The corresponding controllability on a dense domain is called analytic controllability. With the assumption that the Lie algebras generated by these operators are of constant finite-dimension, sufficient conditions for strong analytic controllability of time-dependent quantum control systems are developed. Furthermore, the realization and representation of so(4, 2) associated with the hydrogen atom Hamiltonian are derived. Then by choosing operators from the realization of so (4, 2) as interacting Hamiltonians, a hydrogen atom control system is constructed, and it is proved that this control system is strongly analytically controllable. |
