This chapter presents a detailed study of wavepacket propagation in various physical situations. This approach provides an intuitive understanding of quantum transport and its semiclassical limit. The chapter addresses the transmission formalism, which treats transport through a small conductor connected to electrodes. It introduces the Landauer–Buttiker formulation of transport, based on the quantum transmission of wavepackets through a conductor connected to electrodes. This formalism is very well suited to the study of electron transport through a small system connected to macroscopic electrodes. The chapter presents a step-by-step introduction to the Green's function method, which allows calculating the quantum transmission efficiently. It highlights the link between the Green's function and wavepacket propagation. Stationary states built from the Green's functions can be viewed as wavepackets with a spatial extension tending to infinity. Simulating transient regimes and noise is of great importance for technological applications.

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