By employing a simple step potential as the interaction potential in a collision between an atom and a diatomic molecule, we develop a full quantum mechanical treatment of vibrational energy transfer in a collinear collision for which the resulting coupled differential equations can be solved exactly. We find that for all but the weakest coupling strengths, the trend of the solutions to their converged value is not smooth and monotonic but rather shows large oscillations. We also locate a region in the parameter space in which the solutions are a very sensitive function of the coupling strength showing something analogous to rsquo;rsquo;resonantrsquo;rsquo; behavior.
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