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Poisson's Equation

A second-order partial differential equation arising in physics,

del ^2psi=-4pirho.

If rho=0, it reduces to Laplace's equation.

It is also related to the Helmholtz differential equation

del ^2psi+k^2psi=0.

See also

Helmholtz Differential Equation, Laplace's Equation, Vector Poisson Equation

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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.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 271, 1953.Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 417, 1995.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 129, 1997.

Referenced on Wolfram|Alpha

Poisson's Equation

Cite this as:

Weisstein, Eric W. "Poisson's Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PoissonsEquation.html

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