PHYS 343: Piecewise constant potentials

Figure 1

A Gaussian wavepacket incoming from the left hits a potential wall. The mean energy of the wavepacket is E=1.2 V₀, i.e., it has enough energy to travel across the wall. Position x is given in units of ℏ/√(2 m V₀)

Figure 2

A Gaussian wavepacket incoming from the left hits a potential wall. The mean energy of the wavepacket is E=0.8 V₀. A classical particle would be fully reflected by the wall. Parts of the wavepacket can leak into the classically forbidden region (skin effect)

Figure 3

A Gaussian wavepacket incoming from the left hits a potential barrier of width L. The mean energy of the wavepacket is E=1.2 V₀. You can see interference between incoming and reflected parts of the wavepackets when L is a multiple the de Broglie wavelength of a partial wave.

Figure 4

A Gaussian wavepacket incoming from the left hits a potential barrier of width L. The mean energy of the wavepacket is E=0.93 V₀. S small part of the wavepacket is transmitted. This is quantum tunnelling