Time-dependent Schrödinger Equation based on HO-FDTD Schemes

A high order finite-different time-domain methods using Taylor series expansion for solving time-dependent Schrodinger equation has been systematically discussed in this paper. Numerical characteristics have been investigated of the schemes for the Schrodinger equation. Compared with the standard Yee FDTD scheme, the numerical dispersion has been decreased and the convergence has been improved. The general update equations of the methods have been presented for wave function. Numerical results of potential well in one-dimension show that the application of the schemes is more effective than the Yee’s FDTD method and the higher order has the better numerical dispersion characteristics.