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In this paper we will demonstrate the use of Feynman Diagrams for onedimensional scattering in quantum mechanics. We will evaluate the S-Matrixexplicitly for the Dirac delta and finite wall potentials by summing the fullseries of Feynman diagrams, illustrating the spirit of perturbation theory.This technique may be useful in introductory quantum mechanics courses, andprovides the student with intuition about conservation laws in the context ofscattering problems by connecting Feynman diagrams, free propagation, andconservation of the corresponding observable. It also provides a toy model forcalculating S-matrix elements in quantum field theory.

Delta Function Scattering with Feynman Diagrams in 1d Quantum Mechanics