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单词 Effective potential
释义

Effective potential

中文百科

等效位能

等效位能是将许多效应综合成单一位能的数学表达式。在古典力学中,等效位能即为离心力位能与位能的和。等效位能常被用来计算行星的轨道及半古典的原子计算,可用来降低问题的维度。

等效位能 U_\text{eff} 可定义如下:

 U_\text{eff}(\mathbf{r}) = \frac{L^2}{2mr^2} + U(\mathbf{r})

L 为角动量。
r 为两物体之距离。
m 为绕行物体之质量。
U(r) 为位能。

等效力,也就是等效位能的梯度取负号则为:

 \begin{align}
\mathbf{F}_\text{eff} &= -\nabla U_\text{eff}(\mathbf{r}) \\
                      &= \frac{L^2}{mr^3}\hat{\mathbf{r}} - \nabla U(\mathbf{r})
\end{align}

其中 \hat{\mathbf{r}} 为r方向的单位矢量。

英语百科

Effective potential 等效位能

The effective potential (also known as effective potential energy) is a mathematical expression combining multiple (perhaps opposing) effects into a single potential. In classical mechanics it is defined as the sum of the 'opposing' centrifugal potential energy with the potential energy of a dynamical system. It is commonly used in calculating the orbits of planets (both Newtonian and relativistic) and in semi-classical atomic calculations, and often allows problems to be reduced to fewer dimensions.

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更新时间:2025/6/17 17:20:11