Atom-diatom collisions in the momentum space representation: a connection between quantum and classical expressions

The impulsive collinear collision of an atom and diatomic molecule, modelled as a harmonic oscillator, is expressed in the momentum space representation of quantum mechanics. We find an interesting connection between the quantum and the classical picture (assuming the oscillator to be quantized) and a faster convergence in the quantum mechanical numerical solution. In addition, it provides an analytic approximation that is valid for systems initially in the vibrational ground state, which is analogous to the Franck-Condon overlap integrals.