Bilingual edition: English is preserved and Chinese follows each unit. Terminology uses the confirmed v20260916 glossary; automated semantic review remains traceable.
中英双语版：英文原文完整保留，中文紧随对应单元；术语采用 v20260916 确认表，自动语义审校结果可追溯。

The LaPlacian

拉普拉斯算子

The divergence of the gradient of a scalar function is called the Laplacian. In rectangular coordinates:

The Laplacian finds application in the Schrodinger equation in quantum mechanics. In electrostatics, it is a part of LaPlace's equation and Poisson's equation for relating electric potential to charge density.

LaPlacian in other coordinate systems

其他坐标系中的拉普拉斯算子
标量函数的梯度的散度称为拉普拉斯算子。在直角坐标系中：拉普拉斯算子在量子力学中的薛德方程中有所应用。在静电学中，它是拉普拉斯方程和泊松方程的一部分，用于将电势与电荷密度联系起来。
 Index

Vector calculus
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Laplacian, Various Coordinates

拉普拉斯，各种坐标

Compared to the LaPlacian in rectangular coordinates:

In cylindrical polar coordinates:
and in spherical polar coordinates:
与直角坐标系中的拉普拉斯算子相比：在柱坐标系中：以及在球坐标系中：
 Index

Vector calculus
索引 矢量微积分
 
HyperPhysics*****HyperMath*****Calculus
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