The LaPlacian

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

 Index

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Laplacian, Various Coordinates

Compared to the LaPlacian in rectangular coordinates:

In cylindrical polar coordinates:
and in spherical polar coordinates:
 Index

Vector calculus
 
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