Helmholtz equation
Eigenvalue problem for the Laplace operator / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Helmholtz equation?
Summarize this article for a 10 year old
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]