V2EX radial equation

Radial Equation

释义 Definition

“Radial equation” 指径向方程:在具有球对称或圆对称的问题中,把方程按“径向(离中心的距离)”变量单独分离后得到的方程,常见于拉普拉斯方程、薛定谔方程、波动方程等的变量分离法中。(在量子力学里常特指氢原子等体系的径向薛定谔方程。)

发音 Pronunciation (IPA)

/redil kwen/

例句 Examples

The radial equation describes how the wavefunction changes with distance from the center.
径向方程描述波函数如何随离中心的距离而变化。

After separating variables in spherical coordinates, we solve the angular part and then the radial equation to find the allowed energy levels.
在球坐标中分离变量后,我们先解角向部分,再解径向方程以得到允许的能级。

词源 Etymology

“Radial” 来自拉丁语 radius(意为“辐条、半径、光线”),引申为“沿半径方向的、径向的”。“Equation” 来自拉丁语 aequatio(意为“使相等、均衡”),对应“等式/方程”的概念。合起来即“关于径向变量的方程”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Introduction to Quantum Mechanics(David J. Griffiths, 量子力学教材中讨论中心势问题时出现“radial equation”)
  • Mathematical Methods for Physicists(Arfken, Weber & Harris,在球坐标分离变量与特殊函数章节中出现)
  • Methods of Theoretical Physics(Morse & Feshbach,在偏微分方程分离变量与球对称问题中出现)
  • Quantum Mechanics(Cohen-Tannoudji 等,在氢原子与中心势的径向方程推导中出现)
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