Abstract
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We obtained the potential scattering amplitude from the complete Green function in the corresponding external field through solving the Schrodinger equation, after being separated from the poles on the mass shell, which takes the form of an eikonal (Glauber) representation in the high energy region and the small scattering angles. Considering specific external potentials such as the Yukawa or Gaussian potential, we found the corresponding differential scattering cross-sections.
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