Abstract: In a quantum system,when the Hamiltonian operator is time-dependent,"artificial" variables are introduced to construct the symplectic integrators with arbitrary high order accuracy.As an example,the time-evolution of an electron in the infinite deep potential well interacting with an animated laser field is investigated.The computed results coincide with the theory and can preserve the norm,which show that the methods are reasonable.

Key words: symplectic integrator, PRK method