The meaning of path integral formulation

There are different ways of describing quantum mechanics, such as Schrodinger’s equations, Heisenberg’s matrix mechanics. In the textbook Advanced quantum mechanics by Sakurai, the known method of canonical quantization is used, which mainly uses operators, quantum states, wave functions, etc. The other equivalent method is the path integral. But what does it mean?

The path integral is a generalization and formulation method of quantum physics that extends from the principle of action in classical mechanics. It replaces the single path in classical mechanics with the quantum amplitude obtained by including the sum of all paths between two points or the functional integration.

If we divide the whole finite time period into many, many pieces, and the same approach can be applied to each period. Then let these time segments tend to zero, and the number of segments tends to infinity, add them up to find the limit. Finally, it is possible to derive the Schrodinger equation. Feynman's path integral is the generalization of "the principle of least action" in quantum mechanics.

Path integral bridges the gap between classical physics and quantum physics. On the macro scale, the interaction quantum ℏ is a very small quantity. Therefore, for each route, S is much larger than ℏ. Here S is the action. For the adjacent paths of the route, the phase change is very large, which makes these paths contribute The odds and widths overlap each other and cancel each other out.

However, there is a path near the probability range that will not completely cancel out. That is the path when the phase change between this path and its neighboring path is not substantially the same, in other words, the path where the phase variation is 0. Having said that, we already know that it is the path of the classical particle! As a result, quantum problems have transitioned to the classical, which is a deeper relationship between the principle of least action and the path integral of quantum mechanics.

The meaning of path integral formulation相关推荐

学习笔记（Deep Learning for Feynman’s Path Integral in Strong-Field Time-Dependent Dynamics）
文章题目:Deep Learning for Feynman's Path Integral in Strong-Field Time-Dependent Dynamics 原文链接:https:// ...
matlab 路径积分法,数值路径积分法,numerical path integral solution method,音标,读音,翻译,英文例句,英语词典...
补充资料:数值积分法仿真数值积分法仿真 simulation with numerical integration method 具有单点初值的系统来说,仿真计算难以自启动,为此需要用单步法来帮助; ...
Path signature介绍
path signature path signture是描述path的一种特征,它已经在模式识别.异常行为检测.手写识别等领域得到了广泛的运用.现给出path signature的介绍如下: pa ...
实时障碍更新局部路径寻优算法矢量地图数据局部路径规划解集_自动驾驶近期行为预测和规划的一些文章介绍（下）...
继续介绍最近公开的文章. "Driving with Style: Inverse Reinforcement Learning in General-Purpose Planning fo ...
Toward a More Complete, Flexible, and Safer Speed Planning for Autonomous Driving via Convex Optimiz
Toward a More Complete, Flexible, and Safer Speed Planning for Autonomous Driving via Convex Optimiz ...
ICRA 2022 优秀论文
ICRA 2022 Outstanding Paper Translating Images into Maps (WINNER)[code] Saha, Avishkar; Mendez Maldo ...
深度增强学习方向论文整理
from:https://zhuanlan.zhihu.com/p/23600620 作者:Alex-zhai 链接:https://zhuanlan.zhihu.com/p/23600620 来源: ...
DeepWriterID：不依赖书写内容的书写人识别
点击上方"AI搞事情"关注我们 paper: <DeepWriterID: An End-to-end Online Text-independent Writer Ide ...
NeurIPS 2020有哪些值得读的「图神经网络」论文？
在碎片化阅读充斥眼球的时代,越来越少的人会去关注每篇论文背后的探索和思考.在这个栏目里,你会快速 get 每篇精选论文的亮点和痛点,时刻紧跟 AI 前沿成果.如果你也希望让自己的科研成果被更多人看到, ...

The meaning of path integral formulation

The meaning of path integral formulation相关推荐

最新文章

热门文章