On the Formulation of the Feynman Path Integral Through Broken Line Paths
On the Formulation of the Feynman Path Integral Through Broken Line Paths
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关于折线路径费曼路径积分的表述
DOI：
10.1007/s002200050189
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发表时间：
1997
影响因子：
2.4
通讯作者：
W. Ichinose
中科院分区：
文献类型：
--
作者：
W. Ichinose
摘要：研究了非相对论量子力学中通过折线路径的费曼路径积分的表达式。这个公式我们非常熟悉，而且众所周知是有用的。但除了特殊情况外，它的严格意义很少被赋予。本文利用差分方法理论和伪微分算子理论中的思想，严格地证明了对于某一类势，这个公式是定义良好的，并且这个费曼路径积分给出了概率振幅，即Schrödinger方程的解。
Abstract:We study the formulation of the Feynman path integral through broken line paths in non-relativistic quantum mechanics. This formulation is very familiar to us and well known to be useful. But its rigorous meaning is given little except for special cases. In the present paper, using the ideas in the theory of difference methods and the theory of pseudo-differential operators, we show rigorously for some class of potentials that this formulation is well defined and that this Feynman path integral gives the probability amplitude, i.e., the solution of the Schrödinger equation.