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Once again the PhET interactive simulation may be used.

Run the simulation but this time select barrier/well 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.

You can use the mouse to change the height and width of the barrier as well as the total energy and the potential energy.

For different barrier heights and widths, make the same observations as before (Sections 14.13 and 14.16). Note, in particular, the phenomenon of tunnelling when the enegry of the incident particle is less than the barrier height. You can also investigate a well by draging the top of the well downwards (making the V₂ potential negative).

Bound states

To investigate a finite potential well you can run the PhET interactive simulation confining yourself to the One Well tab. Select Square for the Potential Well on the top right.
You can vary the mass of the particle confined in the well and you may display either the Probability Density or the Wave Function (real part, imaginary part, magnitude, phase).

Note that a number of other differently shaped wells (Asymmetric, 2D Coulomb, 3D Coulomb, Harmonic Oscillator) may be studied using this simulation.

Quantum tunnelling

A video animation from  provides an interesting explanation of the phenomenon of .