  We extend the notion of the transfer matrix of potential scattering to a
large class of long-range potentials $v(x)$ and derive its basic properties. We
outline a dynamical formulation of the time-independent scattering theory for
this class of potentials where we identify their transfer matrix with the
$S$-matrix of a certain effective non-unitary two-level quantum system. For
sufficiently large values of $|x|$, we express $v(x)$ as the sum of a
short-range potential and an exactly solvable long-range potential. Using this
result and the composition property of the transfer matrix, we outline an
approximation scheme for solving the scattering problem for $v(x)$. To
demonstrate the effectiveness of this scheme, we construct an exactly solvable
long-range potential and compare the exact values of its reflection and
transmission coefficients with those we obtain using our approximation scheme.
