Moving Particle

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We study the motion of a particle passing through a set of constant potential zones. The initial state is a Gaussian wave packet. The energy of the particle is between the minimum value $E_{\min}$ and the maximum value $E_{\max}$ . Depending on the potential U of the zone, the (average) wavelength varies according to the well-known de Broglie relation $λ = \frac{h}{p}$ where h is Plack's constant and the "parameter p" is given by the relation $p = \sqrt{2 m (E - U)}$ . Recall that the value of the "parameter p" can be interpreted as "momentum" only where the value of the wavelength $λ$ is constant over an length interval L >> $λ$ .
	No Potential HD video Snapshots	The particle moves in the absence of potential, no potential.
	Step Up High HD video Snapshots	The particle collides with a potential step up higher than its energy and reverses the direction of motion. If the potential step were infinite, the result would be the same. The average wavelength does not change because its energy does not change.
	Step Up Low HD video Snapshots	The particle crosses a potential step up lower than its energy. A portion of the wave crosses the step and a portion is reflected. The portion that passes the step has a longer wavelength since it has decreased kinetic energy.
	Step Down HD video Snapshots	The particle crosses a potential step down. Most of the wave passes the step and a small portion is reflected. The portion that passes the step has a shorter wavelength as the kinetic energy is increased.
	Thin Barrier High (Tunnel Effect) HD video Snapshots	The particle collides with a potential thin barrier higher than its energy. Part of the wave passes through the barrier although the energy of the particle is less than the height of the potential barrier (Tunnel Effect). This effect occurs only when the barrier is thin enough. In this case the width of the barrier is 0.2. NOTE: to make the barrier visible, we have drawn it with a greater thickness.
	Thick Barrier High HD video Snapshots	The particle collides with a potential thick barrier higher than its energy and reverses the direction of motion. In this case the barrier is thick and the tunnel effect does not occur. In this case the width of the barrier is 10 (ie 50 times larger than the previous case).
	Thin Barrier Low HD video Snapshots	The particle collides with a potential thin barrier lower than its energy. Since the barrier is very thin (width=0.2), only a small portion of the wave is reflected. NOTE: to make the barrier visible, we have drawn it with a greater thickness.
	Medium Barrier Low HD video Snapshots	The particle collides with a potential medium barrier lower than its energy. Since the width of the barrier (width = 2) is greater than the previous case (width = 0.2), a greater portion of the wave is reflected.
	Thick Barrier Low HD video Snapshots	The particle collides with a potential thick barrier lower than its energy. Since the width of the barrier is very large (width=2) we see a double reflection, one caused by the first and one caused by the second change in potential.
	Narrow Well HD video Snapshots	The particle passes through a potential narrow well (width=10). A portion of the wave crosses the step and a portion is reflected.
	Wide Well HD video Snapshots	The particle passes through a potential wide well. A portion of the wave crosses the step and a portion is reflected. Since the width of the well is very large (width=80) we see a double reflection, one caused by the first and one caused by the second change in potential. The depth of the well is -0.5.
	Deep Wide Well HD video Snapshots	The particle passes through a potential deep wide well (width=80). Similar case to the previous one, but here the depth is -3, while in the previous case the depth is -0.5. As the particle passes over the well, it takes on greater kinetic energy, so the wavelength becomes shorter.