  A new formulation of potential scattering in quantum mechanics is developed
using a close structural analogy between partial waves and the classical
dynamics of many non-interacting fields. Using a canonical formalism we find
non-linear first-order differential equations for the low energy scattering
parameters like scattering length and effective range. They significantly
simplify typical calculations, as we illustrate for atom-atom and
neutron-nucleus scattering systems. A generalization to charged particle
scattering is also possible.
