Computation of quantum system by second-order matrix symplectic scheme

Abstract

In this article the work of Vazquez and Zhang Meiqing et al. has been developed in such a way that it can be used to calculate time evolution of quantum system. In Heisenberg picture, operator symplectic schemes have been changed into matrix symplectic schemes by use of the expansion method, the matrix schemes satisfy equal time commutation relation (ETCR) in the matrix form. The second-order matrix scheme is used to calculate one-dimensional nonlinear harmonic oscillator. The calculated result is compared with results obtained by Runge–Kutta scheme. Calculated results show that results computed by ETCR-preserving and symplectic scheme is consistent with physics theory. It also shows that it is rational and effective as well as reliable to use ETCR-preserving symplectic scheme to calculate time evolution of quantum system in Heisenberg picture. It is proved that second-order symplectic scheme has more computing accuracy than does first-order symplectic scheme. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003