@article{discovery10061820,
            note = {This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions.},
          volume = {66},
         journal = {Progress In Electromagnetics Research M},
           pages = {109--118},
           title = {Symplectic pseudospectral time-domain scheme for solving time-dependent schr{\"o}dinger equation},
            year = {2018},
             url = {http://ceta.mit.edu/pierm/pier.php?paper=18010808},
          author = {Shen, J and Sha, WEI and Kuang, X and Hu, J and Huang, Z and Wu, X},
            issn = {1098-8963},
        abstract = {A symplectic pseudospectral time-domain (SPSTD) scheme is developed to solve Schr{\"o}dinger equation. Instead of spatial finite differences in conventional finite-difference time-domain (FDTD) methods, fast Fourier transform is used to calculate spatial derivatives. In time domain, the scheme adopts high-order symplectic integrators to simulate time evolution of Schr{\"o}dinger equation. A detailed numerical study on the eigenvalue problems of 1D quantum well and 3D harmonic oscillator is carried out. The simulation results strongly confirm the advantages of the SPSTD scheme over the traditional PSTD method and FDTD approach. Furthermore, by comparing to the traditional PSTD method and the non-symplectic Runge-Kutta (RK) method, the explicit SPSTD scheme, which is an infinite order of accuracy in space domain and energy-conserving in time domain, is well suited for a long-term simulation.}
}