势散射路径积分描述中的变分近似
Variational Approximations in a Path-Integral Description of Potential Scattering
摘要：
使用最近的路径积分表示的非相对论性势散射的T-矩阵，我们研究在这个框架下的新的变分近似。通过Feynman-Jensen变分原理和速度变量中最一般的反二次方程--在其上必须进行函数积分--我们得到包含经典元素（轨迹）和量子力学元素（波扩散）的变分方程。我们分析这些方程并用迭代法数值求解，迭代法最适合于高能情况。第一个修正所产生的累积展开的变分结果也进行了评估。比较准确的分波结果从高斯势散射和更好的协议被发现在大的散射角的标准eikonal型近似失败。
英文摘要：
Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables -- over which one has to integrate functionally -- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading).We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.
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