1. We will explore applications of differential geometry in quantum mechanics.  We will move from concrete examples (quantum mechanics of electrons in a bent sheet of graphene) through more abstract ones(quantum mechanics in electric and magnetic fields).  We will explore the geometry of control-parameter space in adiabatic processes.  Finally, we will consider the geometry of momentum space and get insight into polar solids, anomalous Hall effects, and topological insulators. 
   

2. 
   

No prior geometry or differential geometry needed.

Lecture Notes: geometry.pdf

Homework 1 (Due Wednesday April 16): geometryhw1.pdf

Homework 2 (Short -- May Change -- Nominally Due Friday April 18):

geometryhw2.pdf

Homework 3 (May Change -- Due Wednesday April 23):

geometryhw3.pdf

Homework 4 -- Due Wednesday May 7:

geometryhw4.pdf