Packet 13: Bonus 3
In systems like the quantum harmonic oscillator, types of these functions denoted “creation and annihilation” or “a and a dagger” can be used to move between energy levels. For 10 points each:
[10m] Name these functions. In quantum mechanics, observables like position can be associated with self-adjoint, linear versions of these functions.
ANSWER: operators [accept ladder operators or creation operator or annihilation operator or position operator]
[10e] Famously, the position operator does not commute with the operator corresponding to this observable. In classical mechanics, this quantity is set equal to mass times velocity.
ANSWER: momentum
[10h] An important result in quantum mechanics is that all operators that correspond to observables are Hermitian, meaning that these scalars are always real. In the time-independent Schrodinger equation, the energy operator’s values for these scalars are multiplied by the wavefunction.
ANSWER: eigenvalues [accept energy eigenvalues]
<Science - Physics, Omkar Marathe> | VAULT II Packet 13 (Finals 1)
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 7 | 18.57 | 100% | 43% | 43% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Not Just Biking | Armand duplantis fan club | 10 | 10 | 0 | 20 | ME |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at UCSB | 2026-03-13 | ✓ | 1 | 30.00 | 100% | 100% | 100% |
| VAULT II Northern UK | 2026-04-24 | ✓ | 1 | 20.00 | 100% | 100% | 0% |
| VAULT II at Harvard | 2026-04-30 | ✓ | 4 | 15.00 | 100% | 0% | 50% |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 1 | 20.00 | 100% | 100% | 0% |