In the framework of the method of a short-range potential, a study is made of the dissociation of negative ions in a collision, A + B-, and their creation in scattering, A + B + e. In contrast to earlier papers, the motion of the atoms is treated quantum-mechanically. If one makes the natural assumption that the term of the system AB depends weakly on the internuclear distance, the problem reduces to the solution of Helmholtz's equation on a halfplane with mixed boundary condition that depends linearly on the coordinate. An exact analytic solution of this problem is found. A formula is derived for the dissociation cross section near the reaction threshold. The conditions are investigated under which the formulas go over into those previously obtained for classical motion of the atoms.