Nanoelectronic Modeling Lecture 09: Open 1D Systems - Reflection at and Transmission over 1 Step

One of the most elemental quantum mechanical transport problems is the solution of the time independent Schrödinger equation in a one-dimensional system where one of the two half spaces has a higher potential energy than the other. The analytical solution is readily obtained using a scattering matrix approach where wavefunction amplitude and slope are matched at the interface between the two half-spaces. Of particular interest are the wave/particle injection from the lower potential energy half-space.