B-Spline with Symplectic Algorithm Method for Solution of Time-Dependent Schrödinger Equations

A B-spline with the symplectic algorithm method for the solution of time-dependent Schrödinger equations (TDSEs) is introduced. The spatial part of the wavefunction is expanded by B-spline and the time evolution is given in a symplectic scheme. This method allows us to obtain a highly accurate and stable solution of TDSEs. The effectiveness and efficiency of this method is demonstrated by the high-order harmonic spectra of one-dimensional atoms in comparison with other references.