Sommerfeld radiation condition

Arnold Sommerfeld defined the condition of radiation for a scalar field satisfying the Helmholtz equation as Arnold Sommerfeld defined the condition of radiation for a scalar field satisfying the Helmholtz equation as Mathematically, consider the inhomogeneous Helmholtz equation where n = 2 , 3 {displaystyle n=2,3} is the dimension of the space, f {displaystyle f} is a given function with compact support representing a bounded source of energy, and k > 0 {displaystyle k>0} is a constant, called the wavenumber. A solution u {displaystyle u} to this equation is called radiating if it satisfies the Sommerfeld radiation condition