In mathematics, the limiting amplitude principle is a concept from operator theory and scattering theory used for choosing a particular solution to the Helmholtz equation.
The principle was introduced by Andrey Nikolayevich Tikhonov and Alexander Andreevich Samarskii.
[1] It is closely related to the limiting absorption principle (1905) and the Sommerfeld radiation condition (1912).
[2] To find which solution to the Helmholz equation with nonzero right-hand side with some fixed
A particular solution to the Helmholtz equation corresponding to outgoing waves is obtained as the limit for large times.