Bonus
The second adiabatic invariant equals one over two pi times this operation applied to momentum. For 10 points each:
[10h] Propagators are central to a formulation of quantum mechanics named for what operation, which generalizes the principle of least action and was formalized by Richard Feynman?
ANSWER: path integral [or line integral; accept the integral around a closed loop; accept contour integral; prompt on integral or integral with respect to space or integral with respect to position]
[10e] The second adiabatic invariant is quantized in the so-called “old quantum theory” named for Arnold Sommerfeld and this Danish physicist who modeled atoms as electrons orbiting a nucleus.
ANSWER: Niels Bohr
[10m] In the path integral formulation, one finds a process’s amplitude of this quantity by integrating over possible paths. The squared modulus of the wavefunction equals the density of this quantity by Born’s rule.
ANSWER: probability [accept probability amplitude; accept probability density]
<Editors, Physics>
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 2 | 106 | 14.62 | 95% | 32% | 19% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Guelph A | Waterloo B | 0 | 10 | 0 | 10 | E |
| McMaster A | Toronto C | 0 | 10 | 0 | 10 | E |
| McMaster C | Toronto H | 0 | 10 | 10 | 20 | EM |
| Toronto A | Toronto D | 10 | 10 | 10 | 30 | HEM |
| Toronto B | Waterloo A | 0 | 10 | 0 | 10 | E |
| Toronto F | Brock A | 0 | 10 | 10 | 20 | EM |
| Toronto G | McMaster B | 0 | 10 | 0 | 10 | E |
| Toronto I | Queen's A | 0 | 0 | 0 | 0 | |
| Waterloo C | Toronto E | 0 | 10 | 10 | 20 | EM |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| UK (North) | UK | Y | 5 | 14.00 | 100% | 20% | 20% |
| UK (South) | UK | Y | 8 | 18.75 | 100% | 50% | 38% |
| Southern California | US | Y | 7 | 17.14 | 100% | 43% | 29% |
| Eastern Canada (2) | US | Y | 9 | 14.44 | 89% | 44% | 11% |
| Great Lakes | US | Y | 12 | 14.17 | 100% | 33% | 8% |
| Lower Mid-Atlantic | US | Y | 6 | 8.33 | 83% | 0% | 0% |
| Upper Mid-Atlantic | US | Y | 12 | 15.83 | 92% | 42% | 25% |
| Midwest | US | Y | 9 | 13.33 | 100% | 33% | 0% |
| Northeast | US | Y | 12 | 15.00 | 100% | 25% | 25% |
| Pacific | US | Y | 9 | 16.67 | 89% | 44% | 33% |
| Southeast | US | Y | 12 | 13.33 | 92% | 17% | 25% |
| Upstate NY | US | Y | 5 | 12.00 | 100% | 20% | 0% |