Mathematica exercises of introduction to Mesoscopic physics

During the fall terms of 2010 and 2011, in collaboration with Dr. Daniel Urban (now at the IWM-Fraunhofer Institute Freiburg), I gave an “Introduction to Nanoelectronics” class. Practical Wolfram Mathematica® exercises complemented this class. Here I propose, together with the solution, the exercises sheet Daniel and I offered to our students:

Exercise 0 — An elementary Introduction to Wolfram Mathematica or Wolfram Language.

Exercise 1 (Solution) — Single-particle in a one-dimensional potential.

Exercise 2 (Solution) — Scattering against a single and a double rectangular potential barrier. 

Exercise 3 (Solution) — Transfer matrix and scattering matrix methods for scattering against multiple barriers. 

Exercise 4 (Solution) — Scattering against multiple barriers, a transition from the coherent to the incoherent regime.

Exercise 5 (Solution) — Density of States in two- and one-dimensional systems.

Exercise 6 (Solution) — Random matrix theory and analysis of level spacing statistics.

Exercise 7 (Solution) — Spin-Orbit interaction in a two-dimensional electron gas.

Exercise 8 (Solution) — Rashba spin-orbit interaction in a quasi-one-dimensional electron gas.

Exercise 9 (Solution) — The Honeycomb lattice.

Exercise 10 (Solution) — Bloch theorem for a one-dimensional periodic potential.

Exercise 11 (Solution) — Klein tunnelling for the Dirac Hamiltonian.

Exercise 12 (Solution) — Graphene nanoribbons, zigzag and armchair case.

© Dario Bercioux 2022