For 10 points each, answer the following about Bloch’s theorem:
[10m] Bloch’s theorem states that, when this quantity is periodic, solutions to the Schrödinger equation equal a plane wave times a periodic function. This quantity is infinite outside of the walls of a particle in a box.
ANSWER: potential energy [or periodic potential; prompt on U or V]
[10e] Because they can be modeled as a periodic potential, Bloch’s theorem is used to describe the wavefunction of electrons in these materials. They have an ordered, repeating structure, unlike amorphous solids.
ANSWER: crystals [prompt on lattices]
[10h] To obtain a reduced-zone scheme of the energy of electrons in a crystal, the wave vector k in Bloch’s theorem can be restricted to lie within the first of these regions, which are primitive cells in reciprocal space.
ANSWER: first Brillouin zone [bree-yuh-wan zone]
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