 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-2/section-b/21/iv/a/solution

For longitudinal motion in transverse subband

i

ϵ_{i} (k) = E_{i} + \frac{ℏ ^{2} k ^{2}}{2 m}, v (k) = \frac{1}{ℏ} \frac{d ϵ _{i}}{d k} = \frac{ℏ k}{m} .

For a completely free particle take

E_{i} = 0

and use the full wave vector. In a semiconductor the parabolic-band mass is the appropriate effective mass rather than necessarily the bare electron mass.

 New to topics? Read the docs here!