QuantumWell displays a wave function in either a square well or a harmonic oscillator potential (optionally evolving under a small perturbation that leaves the energy of the system unchanged, but is otherwise random). The contours are for the squared magnitude of the wave, with phase indicated by colour.

The **harmonic oscillator** begins with one or more roughly Gaussian wave
packets oscillating back and forth in the potential. These wave packets are created
by translating the oscillator’s Gaussian ground state away from the centre of the well,
and if they were perfectly constructed they would bounce back and forth indefinitely
without changing shape (they do overlap, though, so this is clearest when there’s only
a single wave packet). However, the wave shown here is an approximation, built from a
finite number of energy eigenstates, so the packets are not exactly Gaussian and their
shape will change slightly as they move. In the longer term, they will also be degraded
by any random perturbation that has been selected.

The **square well** begins with a localised wave, a finite-energy approximation
to a randomly chosen rectangular step function. The original shape rapidly disperses,
but will periodically recur (though again, if there is a random perturbation it will gradually
disrupt that behaviour).

**Click on the applet** to pause or redraw. If the applet is not running smoothly, you can
try to get a better frame rate by **reducing the number of modes** from which the wavefunction is built.