  Background: Path integrals are a powerful tool for solving problems in
quantum theory that are not amenable to a treatment by perturbation theory.
Most path integral computations require an analytic continuation to imaginary
time. While imaginary time treatments of scattering are possible, imaginary
time is not a natural framework for treating scattering problems. Purpose: To
test a recently introduced method for performing direct calculations of
scattering observables using real-time path integrals. Methods: The
computations are based on a new interpretation of the path integral as the
expectation value of a potential functional on a space of continuous paths with
respect to a complex probability distribution. The method has the advantage
that it can be applied to arbitrary short-range potentials. Results: The new
method is tested by applying it to calculate half-shell sharp-momentum
transition matrix elements for one-dimensional potential scattering. The
calculations for half shell transition operator matrix elements are in
agreement with a numerical solution of the Lippmann-Schwinger equation. The
computational method has a straightforward generalization to more complicated
systems.
