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The PhET interactive simulation may be used again to study the potential step barrier.

Plane wave

Run the simulation and this time select step for the Potential on the top right. Select plane wave for the Electron Wave Function form and tick the Show energy values and Show reflection and transmission probabilities boxes. Initially view separate Incoming/Reflected waves but it is also interesting to view their sum.

Use the mouse to change the total energy (green line) and/or the potential energy (purple). Observe the effect on the amplitude and on the frequency of the wave. Note, in particular, what happens when the total energy is less than the energy of the potential step.

Observe the imaginary part, the magnitude and the phase of the wave by checking the associated boxes in turn.

Also observe what happens if you reverse the direction of the incoming wave — the 'potential drop' (the total energy must be greater than the step potential in this case).

Wave packet  Select wave packet for the Electron Wave Function form. Once again there is wave packet spreading (recall the free particle Section 14.13).  Use the mouse to change the total energy and/or the potential energy and observe the effect on the wave packet.  Observe the imaginary part, the magnitude and the phase of the wave by checking the associated boxes in turn.

 Potential drop

You can also investigate a potential drop by dragging the step to negative values.