Numerical solutions of Schrdinger equation have become increasingly important because of the tremendous demands for the design and optimization of nanodevices where quantum effects are significant or dominate. Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrdinger equation. A detailed numerical study on 1 D quantum eigenvalue problems is carried out. Compared with FDTD(2,2) and FDTD(2,4), the simulation results of quantum wells and harmonic oscillators strongly confirm that the explicit SFDTD scheme is well suited for a long-term simulation.