Consider the potential barrier illustrated in Figure 1, with V(x) = V₂ in the region 0 < x < L and V(1) = 0 elsewhere. Particles with energy o L. b) Identify the parts of your solutions that correspond to the incident, reflected and transmitted particles. Explain why the remaining term in the region > L can be set to zero. c) Determine the probability currents associated with the incident, reflected and transmitted particles.
Consider the potential barrier illustrated in Figure 1, with V(x) = V₂ in the region 0 < x < L and V(1) = 0 elsewhere. Particles with energy o L. b) Identify the parts of your solutions that correspond to the incident, reflected and transmitted particles. Explain why the remaining term in the region > L can be set to zero. c) Determine the probability currents associated with the incident, reflected and transmitted particles.
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Transcribed Image Text:Consider the potential barrier illustrated in Figure 1, with V(x) = V₁ in the region 0 < x < L and
V(T) = 0 elsewhere. Particles with energy 0 < E<V₁ are incident on the barrier from the left.
E< Vo
V = Vo
V = 0
x = 0
x=L
Figure 1: A potential barrier, with particles incident from the left.
Now do the following:
a) Solve the relevant time-independent Schödinger equation in the following three regions:
(i) r < 0, (ii) 0 < r < L, and (iii) 2 > L.
b) Identify the parts of your solutions that correspond to the incident, reflected and transmitted
particles. Explain why the remaining term in the region > L can be set to zero.
c) Determine the probability currents associated with the incident, reflected and transmitted
particles.
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