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We employ the method used by Barbashov and collaborators in Quantum FieldTheory to derive a path-integral representation of the $T$-matrix innonrelativistic potential scattering which is free of functional integrationover fictitious variables as was necessary before. The resulting expressionserves as a starting point for a variational approximation applied tohigh-energy scattering from a Gaussian potential. Good agreement with exactpartial-wave calculations is found even at large scattering angles. A novelpath-integral representation of the scattering length is obtained in thelow-energy limit.

A New Path-Integral Representation of the $T$-Matrix in Potential Scattering