  Using a recent path integral representation for the T-matrix in
nonrelativistic potential scattering we investigate new variational
approximations in this framework. By means of the Feynman-Jensen variational
principle and the most general ansatz quadratic in the velocity variables --
over which one has to integrate functionally -- we obtain variational equations
which contain classical elements (trajectories) as well as quantum-mechanical
ones (wave spreading).We analyse these equations and solve them numerically by
iteration, a procedure best suited at high energy. The first correction to the
variational result arising from a cumulant expansion is also evaluated.
Comparison is made with exact partial-wave results for scattering from a
Gaussian potential and better agreement is found at large scattering angles
where the standard eikonal-type approximations fail.
