  Using the implicit function theorem we demonstrate that solutions to the
classical part of the relativistic Lippmann-Schwinger equation are in
one-to-one correspondence with those of the energy equation of a relativistic
two-body system. A corollary is that the scattering angle can be computed from
the amplitude itself, without having to introduce a potential. All results are
universal and provide for the case of general relativity a very simple formula
for the scattering angle in terms of the classical part of the amplitude, to
any order in the post-Minkowskian expansion.
