  The transfer matrix ${\mathbf{M}}$ of a short-range potential may be
expressed in terms of the time-evolution operator for an effective two-level
quantum system with a time-dependent non-Hermitian Hamiltonian. This leads to a
dynamical formulation of stationary scattering. We explore the utility of this
formulation in the study of the low-energy behavior of the scattering data. In
particular, for the exponentially decaying potentials, we devise a simple
iterative scheme for computing terms of arbitrary order in the series expansion
of ${\mathbf{M}}$ in powers of the wavenumber. The coefficients of this series
are determined in terms of a pair of solutions of the zero-energy stationary
Schr\"odinger equation. We introduce a transfer matrix for the latter equation,
express it in terms of the time-evolution operator for an effective two-level
quantum system, and use it to obtain a perturbative series expansion for the
solutions of the zero-energy stationary Schr\"odinger equation. Our approach
allows for identifying the zero-energy resonances for scattering potentials in
both full line and half-line with zeros of the entries of the zero-energy
transfer matrix of the potential or its trivial extension to the full line.
