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In this paper, we provide a rigorous quantum mechanical derivation for thecoherent photon transport characteristics of a two-level atom coupled to awaveguide without linearizing the coupling coefficient between the light andthe atom. We propose a novel single frequency sampling method utilizing aUV-cutoff that allows us to treat the singularities in real space scatteringpotential despite the non-convergence property. We also study the conditionsunder which the linearization of the coupling coefficient is an accurateassumption and find the resulting spontaneous emission and transportcharacteristics taking the radiative and non-radiative decay rates intoaccount. This allows us to confirm and expand on the findings of the existingliterature while obtaining the dynamic electronic polarizability for thetwo-level atom confined to a 1-D waveguide while using an interactionHamiltonian with the rotating-wave approximation.

Quantum Mechanical Treatment of Two-Level Atoms Coupled to Continuum with an Ultraviolet Cutoff