Moving Particle

My Quantum Mechanics
Home \ Moving Particle

We study the one dimensional 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 $E_{\max}$ . From the point of view of classical physics, depending on the potential U of the area, the kinetic energy of the classical particle changes and the momentum $p$ changes according to the relation $p = \sqrt{2 m (E - U)}$ . Since the de Broglie relation $λ = \frac{h}{p}$ holds for the quantum particle, it follows that the average wavelength of the packet changes from area to area.
Step by step images	No Potential	The particle moves in the absence of potential, no potential.
Step by step images	Step Up High	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 by step images	Step Up Low	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 by step images	Step Down	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.
Step by step images	Thin Barrier High Tunnel Effect	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.
Step by step images	Thick Barrier High	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).
Step by step images	Thin Barrier Low	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.
Step by step images	Medium Barrier Low	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.
Step by step images	Thick Barrier Low	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.
Step by step images	Narrow Well	The particle passes through a potential narrow well (width=10). A portion of the wave crosses the step and a portion is reflected.
Step by step images	Wide Well	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.
Step by step images	Deep Wide Well	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.