The study of this paper is two-fold:(1)local absorbing boundary conditions(ABCs)are generlized to compute the Schroedinger equation on unbounded domain; then(2)a new asymptotic method based on the frozen Gaussian approximation.The ABCs are dealt that all effects of the Gaussian functions which contribute to the outgoing waves will be eliminated by stopping Hamiltonian flow of their centers when they get out of the domain of interest.