  In this master thesis, a new approximation scheme to non-relativistic
potential scattering is developed and discussed. The starting points are two
exact path integral representations of the T-matrix, which permit the
application of the Feynman-Jensen variational method. A simple Ansatz for the
trial action is made, and, in both cases, the variational procedure singles out
a particular one-particle classical equation of motion, given in integral form.
While the first is real, in the second representation this trajectory is
complex and evolves according to an effective, time dependent potential. Using
a cumulant expansion, the first correction to the variational approximation is
also evaluated. The high energy behavior of the approximation is investigated,
and is shown to contain exactly the leading and next-to-leading order of the
eikonal expansion, and parts of higher terms. Our results are then numerically
tested in two particular situations where others approximations turned out to
be unsatisfactory. Substantial improvements are found.
