Question
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]
<Science - Physics>
Summary
| 2024 Booster Shot (Columbia) | 02/23/2024 | Y | 5 | 16.00 | 100% | 40% | 20% |
| 2024 Booster Shot (Great Lakes) | 03/09/2024 | Y | 6 | 23.33 | 100% | 83% | 50% |
| 2024 Booster Shot (Vanderbilt) | 03/02/2024 | Y | 4 | 10.00 | 75% | 25% | 0% |
| 2024 Booster Shot (WUSTL) | 03/09/2024 | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2024 Booster Shot (Waterloo) | 02/23/2024 | Y | 4 | 27.50 | 100% | 100% | 75% |
Data
| Columbia A | Lehigh B | 10 | 10 | 10 | 30 |
| Gatherer | Bard | 0 | 10 | 0 | 10 |
| NYU A | Columbia B | 0 | 10 | 0 | 10 |
| NYU B | Princeton | 10 | 10 | 0 | 20 |
| Rutgers | Yale | 0 | 10 | 0 | 10 |