Parameterization of all path integral trajectories

Ciann-Dong Yang, Chia Hung Wei

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)118-134
Number of pages17
JournalChaos, solitons and fractals
Volume33
Issue number1
DOIs
Publication statusPublished - 2007 Jul 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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