In mathematics, the eigenvalue problem for the Laplace operator is known as the Helmholtz equation. It corresponds to the linear partial differential equation:
∇
2
f
=
−
k
2
f
{\displaystyle \nabla ^{2}f=-k^{2}f}
where ∇2 is the Laplace operator (or "Laplacian"), 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, including the wave equation and the diffusion equation, and it has uses in other sciences.