路径积分散射的变分方法
Variational Methods for Path Integral Scattering
摘要：
在这篇硕士论文中，我们发展并讨论了一种新的非相对论性势散射近似方案。的出发点是两个精确的路径积分表示的T-矩阵，允许应用的Feynman-Jensen变分法。一个简单的分析的审判行动，并在这两种情况下，变分程序挑出一个特定的单粒子经典运动方程，给出积分形式。虽然第一个是真实的，但在第二个表示中，这个轨迹是复杂的，并且根据有效的、时间依赖的势而演变。使用累积量展开，第一个修正的变分近似也进行了评估。高能量的行为的近似进行了研究，并显示出包含正是领先和次领先的程函展开的顺序，以及部分更高的条款。我们的结果，然后在两个特定的情况下，别人的近似结果是不能令人满意的数字测试。发现了实质性的改进。
英文摘要：
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the Feynman-Jensen variational method. A simple Ansatz for the trial action is made, and, in both cases, the variational procedure singles out a particular one-particle classical equation of motion, given in integral form. While the first is real, in the second representation this trajectory is complex and evolves according to an effective, time dependent potential. Using a cumulant expansion, the first correction to the variational approximation is also evaluated. The high energy behavior of the approximation is investigated, and is shown to contain exactly the leading and next-to-leading order of the eikonal expansion, and parts of higher terms. Our results are then numerically tested in two particular situations where others approximations turned out to be unsatisfactory. Substantial improvements are found.
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