Limiting amplitude principle

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 choice is made by considering a particular time-dependent problem of the forced oscillations due to the action of a periodic force. The principle was introduced by Andrey Nikolayevich Tikhonov and Alexander Andreevich Samarskii. It is closely related to the limiting absorption principle (1905) and the Sommerfeld radiation condition (1912). The terminology -- both the limiting absorption principle and the limiting amplitude principle -- was introduced by Aleksei Sveshnikov.