Helmholtz equation

Summary

The Helmholtz equation is the equation $\Delta u + k^2 u = 0$, where $\Delta$ is the Laplacian and $k$ is a constant called the wave number. It describes waves of a single frequency, and it arises when the time variable is separated in the wave equation. It appears in acoustics, electromagnetism, quantum mechanics and scattering theory. For $k = 0$ it becomes Laplace's equation.