In mathematics, the Helmholtz equation is the eigenvalue problem for the Laplace operator. It corresponds to the linear partial differential equation:
where ∇2 is the Laplace operator, k2 is the eigenvalue, and f is the (eigen)function. When the equation is applied to waves, k is known as the wave number. The Helmholtz equation has a variety of applications in physics and other sciences, including the wave equation, the diffusion equation, and the Schrödinger equation for a free particle.
In optics, the Helmholtz equation is the wave equation for the electric field.[1]
The equation is named after Hermann von Helmholtz, who studied it in 1860.[2]
^Blanche, Pierre-Alexandre (2014). Field guide to holography. SPIE field guides. Bellingham, Wash: SPIE Press. ISBN 978-0-8194-9957-8.
^Helmholtz Equation, from the Encyclopedia of Mathematics.
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