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首页> 外文期刊>The Journal of Chemical Physics >FURTHER ANALYSIS OF SOLUTIONS TO THE TIME-INDEPENDENT WAVE PACKET EQUATIONS OF QUANTUM DYNAMICS .2. SCATTERING AS A CONTINUOUS FUNCTION OF ENERGY USING FINITE, DISCRETE APPROXIMATE HAMILTONIANS
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FURTHER ANALYSIS OF SOLUTIONS TO THE TIME-INDEPENDENT WAVE PACKET EQUATIONS OF QUANTUM DYNAMICS .2. SCATTERING AS A CONTINUOUS FUNCTION OF ENERGY USING FINITE, DISCRETE APPROXIMATE HAMILTONIANS

机译：量子动力学时间独立波包方程解的进一步分析; 2。使用有限离散离散哈密顿函数将散射作为能量的连续函数

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We consider further how scattering information (the S-matrix) can be obtained, as a continuous function of energy, by studying wave packet dynamics on a finite grid of restricted size. Solutions are expanded using recursively generated basis functions for calculating Green's functions and the spectral density operator. These basis functions allow one to construct a general solution to both the standard homogeneous Schrodinger's equation and the time-independent wave packet, inhomogeneous Schrodinger equation, in the non-interacting region (away from the boundaries and the interaction region) from which the scattering solution obeying the desired boundary conditions can be constructed. In addition, we derive new expressions for a ''remainder or error term,'' which can hopefully be used to optimize the choice of grid points at which the scattering information is evaluated. Problems with reflections at finite boundaries are dealt with using a Hamiltonian which is damped in the boundary region as was done by Mandelshtam and Taylor [J. Chem. Phys. 103, 2903 (1995)]. This enables smaller Hamiltonian matrices to be used. The analysis and numerical methods are illustrated by application to collinear H+H-2 reactive scattering. (C) 1996 American Institute of Physics. [References: 32]
机译：我们进一步考虑如何通过研究有限尺寸的有限网格上的波包动力学来获得散射信息（S矩阵），作为能量的连续函数。使用递归生成的基函数来扩展解，以计算格林函数和谱密度算符。这些基础函数允许在非相互作用区域（远离边界和相互作用区域）中构造标准均质薛定inger方程和与时间无关的波包非均质薛定inger方程的通用解遵循期望的边界条件可以被构造。此外，我们导出了“余项或误差项”的新表达式，希望可以将其用于优化对散射信息进行评估的网格点的选择。有限边界处的反射问题可通过使用哈密顿量来解决，该哈密顿量在边界区域被阻尼，这是由曼德尔施塔姆（Mandelshtam）和泰勒（Taylor）[J.化学物理103，2903（1995）]。这使得可以使用较小的哈密顿矩阵。通过对共线H + H-2反应性散射的应用说明了该分析方法和数值方法。 （C）1996年美国物理研究所。 [参考：32]

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