| 书目名称 | Rigorous Time Slicing Approach to Feynman Path Integrals |
| 编辑 | Daisuke Fujiwara |
| 视频video | |
| 概述 | Assumes the potential is such that it is smooth and its derivatives of order equal to or higher than two are bounded.Establishes the proof by the time slicing method, the method Feynman himself used, |
| 丛书名称 | Mathematical Physics Studies |
| 图书封面 |  |
| 描述 | This book proves that Feynman‘s original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved..The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger‘s quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger‘s method, there is still much to be done concerning rigorous mathematical treatment of Feynman‘s method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by dividing the time interval into small pieces. This method is called the time slicing approximation method or the time slicing method..This book consists of two parts. Part I is t |
| 出版日期 | Book 2017 |
| 关键词 | Feynman path integral; Feynman propagator; Fundamental solution; Quantum mechanics; Schroedinger equatio |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-4-431-56553-6 |
| isbn_softcover | 978-4-431-56818-6 |
| isbn_ebook | 978-4-431-56553-6Series ISSN 0921-3767 Series E-ISSN 2352-3905 |
| issn_series | 0921-3767 |
| copyright | Springer Japan KK 2017 |
发表于 2025-3-21 18:19:33
