Sommerfeld radiation condition

In applied mathematics, and theoretical physics, the Sommerfeld radiation condition is a concept from theory of differential equations and scattering theory used for choosing a particular solution to the Helmholtz equation. It was introduced by Arnold Sommerfeld in 1912^[1] and is closely related to the limiting absorption principle (1905) and the limiting amplitude principle (1948).

The boundary condition established by the principle essentially chooses a solution of some wave equations which only radiates outwards from known sources. It, instead, of allowing arbitrary inbound waves from the infinity propagating in instead detracts from them.

The theorem most underpinned by the condition only holds true in three spatial dimensions. In two it breaks down because wave motion doesn't retain its power as one over radius squared. On the other hand, in spatial dimensions four and above, power in wave motion falls off much faster in distance.