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Three methods for the calculation of vibrational transition probabilities in colinear atom–diatomic molecule collisions are outlined. These are based on the approximation of the intermolecular potential by terms which permit the solution of the Schrödinger equation by separation of variables in each of several regions into which the configuration space of the system is divided. Boundary conditions between the regions lead to systems of linear equations the solutions to which yield quantities from which the transition probabilities are easily obtained. Plots of transition probabilities for various repulsive intermolecular potentials are shown and discussed.