  We consider the Sommerfeld problem of diffraction by an opaque half-plane
with a real wavenumber
  interpreting it as the limiting case, as time tends to infinity, of the
corresponding time-dependent diffraction problem. We prove that the Sommerfeld
formula for the solution is the limiting amplitude of the solution of this
time-dependent problem which belongs to a certain functional class and is
unique in it. For the proof of uniqueness of solution to the time-dependent
problem we reduce it, after the Fourier-Laplace transform in $t$, to a
stationary diffraction problem with a complex wavenumber. This permits us to
use the proof of uniqueness in the Sobolev space $H^1$. Thus we avoid imposing
the radiation and regularity conditions on the edge from the beginning and
instead obtain it in a natural way.
