Nanoelectronic Modeling Lecture 10: Open 1D Systems - Transmission through & over 1 Barrier

Tunneling and interference are critical in the understanding of quantum mechanical systems. The 1D time independent Schrödinger equation can be easily solved analytically in a scattering matrix approach for a system of a single potential barrier. The solution is obtained by matching wavefunction values and derivatives at the two interfaces in the spatial domain. This simple example shows the extended nature of wavefunctions, the non-local effects of local potential variations, the formation of resonant states through interference, and quantum mechanical tunneling in its simplest form.