Symplectic integrators for the multichannel Schrödinger equation
Symplectic integrators for the multichannel Schrödinger equation
复制标题
多通道薛定谔方程的辛积分器
DOI：
10.1063/1.468871
复制
发表时间：
1995
影响因子：
4.4
通讯作者：
S. Gray
中科院分区：
文献类型：
--
作者：
D. Manolopoulos;S. Gray
在与时间无关的非弹性散射理论和某些束缚态问题中产生的多通道径向薛定谔方程具有经典的哈密顿结构，其中径向坐标起着时间的作用。这种哈密顿结构的一个结果是薛定谔方程具有辛对称性，这导致在非弹性散射的背景下S矩阵的酉性和对称性。另一个结果是，所谓的辛积分器可以用来解束束态和散射问题的径向薛定谔方程。利用这一思想，导出了一类新的求解多通道径向薛定谔方程的基于辛积分器的对数导数方法。除了编写和编程更简单之外，这些方法在几个非弹性散射和束缚态测试问题上与Johnson的原始对数导数方法具有很强的竞争力。遵循符号版本的等同解决方案。
The multichannel radial Schrodinger equation that arises in time‐independent inelastic scattering theory and certain bound state problems has a classical Hamiltonian structure in which the radial coordinate plays the role of time. One consequence of this Hamiltonian structure is that the Schrodinger equation has symplectic symmetries, which lead in the context of inelastic scattering to the unitarity and symmetry of the S matrix. Another consequence is that so‐called symplectic integrators can be used to solve the radial Schrodinger equation, both for bound state and scattering problems. This idea is used here to derive a new family of symplectic integrator‐based log derivative methods for solving the multichannel radial Schrodinger equation. In addition to being simpler to write down and program, these methods are shown to be highly competitive with Johnson’s original log derivative method for several inelastic scattering and bound state test problems. An equivalent solution following version of the symp...