势散射中$T$ -矩阵的新路径积分表示
A New Path-Integral Representation of the $T$-Matrix in Potential Scattering
摘要：
我们采用Barbashov和合作者在量子场论中使用的方法，导出非相对论势散射中$T$ -矩阵的路径积分表示，它不需要像以前那样在虚拟变量上进行函数积分。由此产生的表达式作为一个起点的变分近似适用于高能量散射从高斯电位。即使在大的散射角与精确的分波计算发现良好的协议。在低能极限下得到了散射长度的一种新的路径积分表示。
英文摘要：
We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a path-integral representation of the $T$-matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit.
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