Run the program and estimate the reflection and transmission coefficients from the pulse heights and widths. Notice that the phase wavelength decreases inside the higher-potential segment. Increase the potential to . The pulse is almost entirely reflected by the step, although it does penetrate the forbidden region. Use the integral of the probability current to show this.
Atomic units simplify many of the relationships between wave and particle properties.
A particle with momentum in a zero-potential region has energy and wavelength . If this particle-wave propagates into a region where , then the kinetic energy increases to and the momentum becomes . Notice that the reflection of the quantum wave packet is almost zero. Use detectors and current integrals to determine the reflection and transmission probabilities.