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] and the Sommerfeld radiation condition.
The terminology -- both the limiting absorption principle and the limiting amplitude principle -- was introduced by Aleksei Sveshnikov.
Formulation
To find which solution to the Helmholz equation with nonzero right-hand sidewith some fixed, corresponds to the outgoing waves,
one considers the wave equation with the source term,
with zero initial data. A particular solution to the Helmholtz equation corresponding to outgoing waves is obtained as the limit
for large times.