论文标题
边界条件和Feynman路径积分的辅助阶段
Boundary Condition and the Auxiliary Phase in Feynman Path Integral
论文作者
论文摘要
当使用Feynman Path积分来计算量子物理中的传播器时，对所有路径集合的概念并不总是天真的。实际上，通常必须将辅助阶段作为每个求和的权重。在本文中，我们讨论了各种边界条件的这些相位因素的性质，包括所有三种Dirichlet，Neumann和Robin类型及其混合物。我们验证，对于限制在线段上的自由粒子，传播器上的结果公式与由schrodinger方程产生的粒子匹配，该公式具有琐碎的归一化因子。
When employing Feynman path integrals to compute propagators in quantum physics, the concept of summing over the set of all paths is not always naive. In fact, an auxiliary phase often has to be included as a weight for each summand. In this article we discuss the nature of those phase factors for the various types of boundary conditions including all three of the Dirichlet, Neumann and Robin types, as well as their mixtures. We verify that for a free particle confined on a line segment, the resulting formula on the propagator matches those arising from the Schrodinger equation, with a trivial normalization factor.
