Homework 1 (due Feb 1)

1. At t=0, sketch the wave-function as a function of x over a few lattice spacings for Bloch states for which:
a) k=0;   b) k=\(\pi/a\);   c) k=\(\pi/2a\);   d) k=\(- \pi/2a\)
e) sketch a graph of the atomic state wave-function you used in your Bloch state construction.
Note that, with time dependence included,  a) and b) represent standing waves, while  c) and d) are traveling waves, traveling to the right and left, respectively.

Physics 232 course outine

This is flexible and open to modification. Your thoughts and input are welcome.

• Semiconductor Physics: Band bending and the ability to manipulate the Fermi level (aka chemical potential) play an important role in semiconductor physics. We will look at characteristics of inhomogeneous semiconductor systems including the non-equilibrium dynamics of p-n junctions.  We could also discuss FETs and 2DEGs if there is interest.
• Matrix approach to crystal quantum mechanics:  -new ways to look at quantum state evolution, -role of disorder in crystals, disorder-driven metal-insulator transition (Anderson localization).
• Mott-Hubbard Model: -modeling e-e interaction, relevance to correlated phenomena, quasi-2D superconductors (cuprates), antiferromagnetism, quantum computing (2 dot qbit)
• Band theory: \(sp^2\) bonding and pz band in graphene and related boride structures?, Dirac point, bands in cuprates?, density functional theory
• Ferromagnetism: breakdown of band theory, role of e-e interaction in spin aligned states...
• ...