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Poisson's Equation

A second-order Partial Differential Equation arising in physics:

\nabla^2\psi =-4\pi\rho.

If $\rho = 0$, it reduces Laplace's Equation. It is also related to the Helmholtz Differential Equation


See also Helmholtz Differential Equation, Laplace's Equation


Arfken, G. ``Gauss's Law, Poisson's Equation.'' §1.14 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 74-78, 1985.

© 1996-9 Eric W. Weisstein