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This research focuses on the possibility of the surjective relation betweensymmetric potential function and its scattering matrix in 1-dimension. Thetheory bases on the property of wave function symmetry and boundary conditions.This research shows the surjective relation in some particular cases, deltafunction potential, and finite square wall potential, and disproves theinjective relation of the arbitrary potential function and its S-matrix.

Verifying the surjective relation between symmetric potential function and its Scattering Matrix in 1D