Computational quantum dynamics (CQD) is an approach to quantum physics in which one tries to solve the time-dependent Schrodinger equation numerically by finite difference method [1-4]. We will present possible examples. of computational quantum dynamics in atomic physics, and discuss the possibilities of the method and the methodological problems to be solved for the wider application of CQD. We also introduce a new numerical method for the calculation of the time evolution of quantum states in the time-dependent Hamiltonian system.