  The de Broglie - Bohm "pilot-wave" theory replaces the paradoxical
wave-particle duality of ordinary quantum theory with a more mundane and
literal kind of duality: each individual photon or electron comprises a quantum
wave (evolving in accordance with the usual quantum mechanical wave equation)
and a particle that, under the influence of the wave, traces out a definite
trajectory. The definite particle trajectory allows the theory to account for
the results of experiments without the usual recourse to additional dynamical
axioms about measurements. Instead one need simply assume that particle
detectors click when particles arrive at them. This alternative understanding
of quantum phenomena is illustrated here for two elementary textbook examples
of one-dimensional scattering and tunneling. We introduce a novel approach to
reconciling standard textbook calculations (made using unphysical plane-wave
states) with the need to treat such phenomena in terms of normalizable wave
packets. This allows for a simple but illuminating analysis of the pilot-wave
theory's particle trajectories, and an explicit demonstration of the
equivalence of the pilot-wave theory predictions with those of ordinary quantum
theory.
