V2EX spherical harmonic

Spherical Harmonic

Definition / 释义

球谐函数:一种定义在球面上的特殊函数族,常用来表示或分解具有球对称(或近似球对称)的物理量与场(如重力场、电磁场、量子力学中的轨道角动量波函数),也是球坐标系下拉普拉斯方程等偏微分方程的典型解之一。(该词在数学、物理与工程中非常常见。)

Pronunciation / 发音

/sfrkl hrmnk/

Examples / 例句

The sound field was approximated using spherical harmonics.
声场用球谐函数进行了近似表示。

In quantum mechanics, the angular part of the hydrogen atom’s wavefunction can be expanded in spherical harmonics, which encode the orbital angular momentum structure.
在量子力学中,氢原子波函数的角向部分可展开为球谐函数,它们刻画了轨道角动量的结构。

Etymology / 词源

spherical 来自 “sphere(球)”,表示“球面的、球形的”;harmonic 源于 “harmony(和谐/谐振)”,在数学与物理里常指与振动、正交分解、频率模式相关的“谐波/调和”结构。合在一起,spherical harmonic 指“在球面上用于分解与表示模式的调和函数”,与傅里叶级数在圆/周期上的分解思想相呼应。

Related Words / 相关词

Literary Works / 文学与作品例证

  • Classical Electrodynamics(J. D. Jackson):多极展开与球谐函数在电磁场问题中的应用
  • Quantum Mechanics(L. D. Landau & E. Lifshitz):角动量与球谐函数的系统论述
  • Methods of Theoretical Physics(P. M. Morse & H. Feshbach):球坐标分离变量、球谐函数与边值问题
  • Mathematical Methods for Physicists(Arfken, Weber & Harris):将球谐函数作为标准工具函数讲解与练习
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