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arXiv physics/0607093physics.chem-ph
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计算原子-硅藻量子反应散射理论中S矩阵的一种新方法

A New Approach To The Evaluation Of The S-Matrix In Atom-Diatom Quantum Reactive Scattering Theory

Ashot S. Gevorkyan, Gabriel G. Balint-Kurti, Gunnar Nyman

摘要:

本文提出了一种计算三维原子-硅藻反应量子散射理论中S矩阵的新方法。该理论是基于自然碰撞坐标发展的,其中沿着反应坐标的进展可以被视为在时间依赖性制剂中履行与时间相同的作用。通过将全波函数写成耦合通道形式,证明了三维量子反应散射问题可以用非弹性单排列问题的同样方式处理。特别是,两种类型的耦合通道表示,这是减少到两个不同的系统耦合的一阶常微分方程描述的非弹性散射,使用。第一个系统的耦合微分方程是在一组点(网格)的坐标反应曲线后,解决了许多一维薛定谔问题的方向垂直于反应坐标。非弹性散射的第二种表达式是利用可精确求解的非定常一维薛定谔方程(标准具方程法)找到的,该方程是为了描述全波函数沿坐标反应曲线的局部化性质而引入的。在这种情况下,我们避免了大量的计算中所涉及的解决一维薛定谔问题沿反应坐标通过使用一个稍微困难的初始条件的非弹性散射方程。在这两种情况下,通过求解耦合的一阶常微分方程组,无需进一步计算,即可同时获得全波函数和所有S矩阵元素。我们的分析表明,我们已经开发的方法构成了最简单的算法计算反应散射S-矩阵。

英文摘要:

A new approach is described to the evaluation of the S-matrix in three-dimensional atom-diatom reactive quantum scattering theory. The theory is developed based on natural collision coordinates where progress along the reaction coordinate can be viewed as fulfilling the same role as time in a time-dependent formulation. By writing the full wavefunction in coupled-channel form it is proved that the 3D quantum reactive scattering problem can be treated in the same way as an inelastic single-arrangement problem. In particularly, two types of coupled-channel representations, which are reduced to two different systems of coupled first order ordinary differential equations describing the inelastic scattering, are used. The first system of coupled differential equations is constructed on a set of points (grid) of the coordinate reaction curve after solution of many 1D Schroedinger problems in the directions normal to the reaction coordinate. The second expression for inelastic scattering is found using exactly solvable nonstationary 1D Schroedinger equation (etalon equation method), which is introduced for describing the localization properties of the full wavefunction along the curve of coordinate reaction. In this case we avoid a large amount of computation involved in solving the 1D Schroedinger problem along the reaction coordinate by using a slightly difficult initial conditions for the inelastic scattering equations. In both cases by solving the system of coupled first order ordinary differential equations, the full wavefunction and all S-matrix elements are obtained simultaneously without further calculations. Our analysis shows that the methods we have developed constitute the simplest algorithms for computing the reactive scattering S-matrices.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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