V2EX potential theory

Potential Theory

释义 Definition

势理论:数学分析的一个分支,研究势函数(potential)及其与拉普拉斯方程/泊松方程调和函数格林函数等的关系;常用于描述与“场”相关的现象(如引力场、电场),并在概率论(如布朗运动)中也有重要联系。

发音 Pronunciation (IPA)

/ptnl θri/

例句 Examples

Potential theory helps explain how electric potential behaves in space.
势理论有助于解释电势在空间中的变化规律。

In complex analysis, potential theory provides powerful tools for studying harmonic functions and boundary value problems.
在复分析中,势理论为研究调和函数与边值问题提供了强有力的工具。

词源 Etymology

potential 原意与“能力、潜能/势能”相关(来自拉丁语 potent- “有力量的、能的”一支),在物理与数学中逐渐专指“势(如电势、引力势)”;theory 来自希腊语 theōria “观察、思考”。合起来的 potential theory 直译为“势的理论”,指围绕“势函数”及其满足的方程体系所形成的方法与理论框架。

相关词 Related Words

文学与著作 Literary Works

  • Ransford, T. Potential Theory in the Complex Plane
  • Helms, L. L. Introduction to Potential Theory
  • Landkof, N. S. Foundations of Modern Potential Theory
  • Doob, J. L. Classical Potential Theory and Its Probabilistic Counterpart
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