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

$$\nabla^2\psi+k^2\psi=0.$$

See also Helmholtz Differential Equation, Laplace's Equation

References

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.