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We propose a novel approach for solving the scattering of light onto atwo-level atom coupled to a one-dimensional waveguide. We first express thephysical quantity of interest in terms of Feynman diagrams and treat the atomas a non-saturable linear beamsplitter. By using the atomic response to ouradvantage, a relevant substitution is then made that captures the nonlinearityof the atom, and the final result is obtained in terms of simple integrals overthe initial incoming wavepackets. The procedure is not limited topost-scattering quantities and allows for instance to derive the atomicexcitation during the scattering event.

Solving the scattering of N photons on a two-level atom without computation