Blanes Sergio, Casas Fernando, Murua Ander
Instituto de Matemática Multidisciplinar, Universitat Politécnica de Valencia, E-46022 Valencia, Spain.
J Chem Phys. 2006 Jun 21;124(23):234105. doi: 10.1063/1.2203609.
We present a family of symplectic splitting methods especially tailored to solve numerically the time-dependent Schrodinger equation. When discretized in time, this equation can be recast in the form of a classical Hamiltonian system with a Hamiltonian function corresponding to a generalized high-dimensional separable harmonic oscillator. The structure of the system allows us to build highly efficient symplectic integrators at any order. The new methods are accurate, easy to implement, and very stable in comparison with other standard symplectic integrators.
我们提出了一族特别定制的辛分裂方法，用于数值求解含时薛定谔方程。在时间上离散化后，该方程可以转化为一个经典哈密顿系统的形式，其哈密顿函数对应于一个广义的高维可分离谐振子。系统的结构使我们能够构建任意阶的高效辛积分器。与其他标准辛积分器相比，新方法精确、易于实现且非常稳定。
