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

Vector calculus

Laplacian, Various Coordinates

Compared to the LaPlacian in rectangular coordinates:

In cylindrical polar coordinates:

and in spherical polar coordinates:

Index

Vector calculus