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We present a detailed study of scattering by an amplitude-modulated potentialbarrier using three distinct physical frameworks: quantum, classical, andsemiclassical. Classical physics gives bounds on the energy and momentum of thescattered particle, while also providing the foundation for semiclassicaltheory. We use the semiclassical approach to selectively add quantum-mechanicaleffects such as interference and diffraction. We find good agreement betweenthe quantum and semiclassical momentum distributions. Our methods and resultscan be used to understand quantum and classical aspects of transport mechanismsinvolving time-varying potentials, such as quantum pumping.

Scattering by an oscillating barrier: quantum, classical, and semiclassical comparison