The exact quantum theory of atomic recombination and collision-induced dissociation (CID) is presented using hyperspherical coordinates. Delves' coordinates are emphasized, methods for doing numerically exact calculations are discussed and implemented, and fully converged dissociation probabilities (J=0) are presented for a model H+Ne-2--> <--H+Ne+Ne system. These are the first accurate CID calculations reported for any atomic system in the full three-dimensional physical space.