1. a) Construct the wave-function of an sp2 state.
b) Do a graph that shows the probability density for that state, e.g., a 2D contour plot or something.
c) Why is the coefficient of the 2s (200) state always \(\sqrt{1/3}\) for an sp2 state?
2. a) What is the Bravias lattic and basis for graphene? How many atoms are in a unit cell?
b) Sketch a picture of the graphene structure and find the coordinates of about 1/2 dozen atoms in that picture.
3. In a perfect hexagon, what are the lengths of all the "chords"? (In terms of the length of a side.) How many chords are there? (It is a small number.)
4. Construct a Bloch state for graphene using only the 2pz orbital. You don't need to solve for anything, but what is the form of such a Bloch state?
Please feel free to ask questions here.
I defined the chord as the distance from one vertex to any other vertex (not including its nearest neighbors).
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