Numerical computation of one-photon mazer resonances for arbitrary field modes

We present a novel approach for solving numerically one-dimensional scattering problems and apply it for computing the emission probability of an ultracold atom interacting with an arbitrary field mode of a high-Q cavity. Our method is efficient, stable and succeeds when other numerical integration methods fail. It also replaces and improves advantageously the WKB approximation. The cases of sinusoidal, sech2 and Gaussian field modes are studied and compared. Divergences with previous works, where WKB was used, are found.