The short-time integrator for propagating the time-dependent Schrödinger equation, which is exact to machine's round off accuracy when the Hamiltonian of the system is time-independent, was applied to solve dynamics processes. This integrator has the old Cayley's form [i.e., the Padé (1,1) approximation], but is implemented in a spectrally transformed Hamiltonian which was first introduced by Chen and Guo. Two examples are presented for illustration, including calculations of the collision energy-dependent probability passing over a barrier, and interaction process between pulse laser and the I(2) diatomic molecule.