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首页> 外文会议>International Workshop on Computer Algebra in Scientific Computing(CASC 2005); 20050912-16; Kalamata(GR) >Symbolic-Numerical Algorithm for Solving the Time-Dependent Schroedinger Equation by Split-Operator Method
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Symbolic-Numerical Algorithm for Solving the Time-Dependent Schroedinger Equation by Split-Operator Method

机译：分裂算子法求解时变薛定inger方程的符号数值算法

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摘要

A new computational approach is proposed for the solution of the time-dependent Schroedinger equation (TDSE), in which a symbolic algorithm named GATEO and a numerical scheme based on the finite-element method (FEM) are effectively composed. The GATEO generates the multi-layer operator-difference scheme for TDSE and evaluates the effective Hamiltonian from the original time-dependent Hamiltonian by means of the Magnus expansion and the Pade-approximation. In order to solve the TDSE with the effective Hamiltonian thus obtained, the FEM is applied to a discretization of spatial domain which brings the difference scheme in operator form to the one in algebraic form. The efficiency and accuracy of GATEO and the numerical scheme associated with FEM is confirmed in the second-, fourth-, and sixth-order time-step computations for certain integrable atomic models with external fields.
机译：针对时间相关的薛定inger方程（TDSE），提出了一种新的计算方法，该方法有效地组成了符号算法GATEO和基于有限元方法的数值格式。 GATEO生成TDSE的多层算子差分方案，并通过Magnus展开和Pade逼近从原始的时变哈密顿量评估有效哈密顿量。为了用由此获得的有效哈密顿量来求解TDSE，将有限元法应用于空间域的离散化，从而将算子形式的差分方案带到代数形式的差分方案。 GATEO的效率和准确性以及与FEM相关的数值方案已在某些具有外部场的可积分原子模型的第二，第四和第六阶时间步长计算中得到确认。

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