Parameterization of all path integral trajectories

Ciann Dong Yang, Chia Hung Wei

研究成果: Article同行評審

16 引文 斯高帕斯(Scopus)

摘要

It is well known that the differentiation of the propagator obtained by path integral formalism leads to the Schrödinger equation. In this paper, we will prove the complementary result that the integration of the Schrödinger equation will lead to the path integral trajectories forming the propagator. The proposed Schrödinger's approach to path integral is helpful in explaining the origin of the multiple quantum paths connecting two fixed points and in providing a means to find all these multiple paths. We point out that path integral trajectories are governed by quantum Hamilton equations derived from the Schrödinger equation and can be continuously parameterized in terms of a free parameter so that an infinite dimensional path integral can be transformed into a one-dimensional normal integral over this free parameter.

原文English
頁(從 - 到)118-134
頁數17
期刊Chaos, solitons and fractals
33
發行號1
DOIs
出版狀態Published - 2007 7月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學(全部)
  • 物理與天文學 (全部)
  • 應用數學

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