Inspect an electron scattering from a rectangular potential barrier. The real wave oscillates while its stationary probability density and transmitted flux follow the boundary-matched solution.
• An incident and reflected region, a rectangular potential barrier, the barrier-region wave, a transmitted region and reflection / transmission counters. • Controls for incident electron energy (eV), barrier height (eV), barrier width (nm) and scattering trials per second. • Four tabs: Quantum bench, Probabilities & measurements, Experiments (with built-in model checks), and Learn & assess.
ℏ²/(2me) = 0.03809982 eV·nm² and k = √(E/0.03809982). For E < V, κ = √[(V−E)/0.03809982] and T = {1 + V² sinh²(κa)/[4E(V−E)]}^−1, with R = 1 − T. For E > V, sinh is replaced by sin and V−E by E−V. The wave and its derivative match at both interfaces.
This is a one-dimensional stationary nonrelativistic electron scattering model with a real rectangular potential and equal exterior potentials. It makes no wavepacket travel-time or tunneling-time prediction and has no many-body or semiconductor band calculation. The carrier phase animation is slowed arbitrarily.
No. A finite barrier permits a nonzero transmitted probability flux.
No. This is a stationary scattering solution with slowed phase animation.
Transmission becomes exponentially small (the "Thick barrier" preset), but the wave is not truncated at the boundary; a thin barrier gives much higher transmission.
Yes. Reflection can still occur above the barrier, and changing the width produces interference resonances (the "Above barrier" preset).