Hamiltonian Feynman path integrals via the Chernoff formula
Hamiltonian Feynman path integrals via the Chernoff formula
复制标题
DOI：
10.1063/1.1500422
复制
发表时间：
2002-09
影响因子：
1.3
通讯作者：
O. Smolyanov;A. Tokarev;A. Truman
中科院分区：
文献类型：
--
作者：
O. Smolyanov;A. Tokarev;A. Truman
本论文的主要目的是使用一个Zeroff定理（即，Schrodinger方程解的Hamiltonian Feynman路径积分（=相空间中轨迹上的Feynman积分）表示的一些严格结果。相应的定理与原来的（费曼）方法费曼路径积分的轨迹在相空间中的方式非常相同的著名定理的纳尔逊是费曼方法费曼路径积分的轨迹在配置空间。我们还给出了一个表示的解决方案的一些薛定谔方程的一系列表示积分的轨迹在相空间中的复泊松测度。
The main aim of the present paper is using a Chernoff theorem (i.e., the Chernoff formula) to formulate and to prove some rigorous results on representations for solutions of Schrodinger equations by the Hamiltonian Feynman path integrals (=Feynman integrals over trajectories in the phase space). The corresponding theorem is related to the original (Feynman) approach to Feynman path integrals over trajectories in the phase space in much the same way as the famous theorem of Nelson is related to the Feynman approach to the Feynman path integral over trajectories in the configuration space. We also give a representation for solutions of some Schrodinger equations by a series which represents an integral with respect to the complex Poisson measure on trajectories in the phase space.