On Convergence of the Feynman Path Integral Formulated Through Broken Line Paths
On Convergence of the Feynman Path Integral Formulated Through Broken Line Paths
复制标题
折线路径形式的费曼路径积分的收敛性
DOI：
10.1142/s0129055x99000313
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发表时间：
1999
影响因子：
1.8
通讯作者：
W. Ichinose
中科院分区：
文献类型：
--
作者：
W. Ichinose
研究了非相对论量子力学中通过折线路径表示的费曼路径积分的收敛性。长期以来，除了特殊情况外，对它的收敛性的严格证明很少。在前一篇论文中，作者证明了对于一类势，这种路径积分是收敛的，并给出了概率幅，即薛定谔方程的解。本文推广了这一结果，给出了某些积分算子在加权Sobolev空间上的有界性定理，并将这一有界性定理与前一文献中的方法结合起来.我们注意到所得结果是规范不变的。
We study the convergence of the Feynman path integral formulated through broken line paths in nonrelativistic quantum mechanics. The rigorous proof of its convergence had been given little except for special cases for a long time. In the preceding paper the author showed for a class of potentials that this path integral converges and gives the probability amplitude, i.e. the solution of the Schrodinger equation. In the present paper we generalize this result, showing the boundedness theorem on the weighted Sobolev spaces for some integral operators and joining this boundedness theorem to the method in the preceding paper. We note that the result obtained is gauge invariant.