  A simple model coupling a one-dimensional beam particle to a one-dimensional
harmonic oscillator is used to explore complementarity and entanglement. This
model, well-known in the inelastic scattering literature, is presented under
three different conceptual approaches, with both analytical and numerical
techniques discussed for each. In a purely classical approach, the final
amplitude of the oscillator can be found directly from the initial conditions.
In a partially quantum approach, with a classical beam and a quantum
oscillator, the final magnitude of the quantum-mechanical amplitude for the
oscillator's first excited state is directly proportional to the oscillator's
classical amplitude of vibration. Nearly the same first-order transition
probabilities emerge in the partially and fully quantum approaches, but
conceptual differences emerge. The two-particle scattering wavefunction
clarifies these differences and allows the consequences of quantum entanglement
to be explored.
