Scattering theory,cross sections,and the lattice of propositions

The asymptotic conditions for the nonrelativistic quantum scattering of a particle by a center of force are derived in terms of a metric on the space of states on a complete orthocomplemented lattice. The flux of particles scattered into a coneC per unit incident flux, averaged over all displacements of the center of force at right angles to the axis of the incident beam, is expressed in terms of the differential cross sectiond/d when the motion is classical, and in terms of the scattering amplitudef when the motion is quantum mechanical. This enables the usual identificationd/d=|f|² to be made.