Question
These objects, which are the typical target of applications of Wick's theorem, are depicted as a gray cat in Griffiths' Introduction to Quantum Mechanics. For 10 points each:
[10h] Name these paired objects that can be written as L-sub-x plus-or-minus i-L-sub-y for angular momentum. These objects can be denoted a and a-dagger.
ANSWER: ladder operators [accept raising AND lowering operators; or creation AND annihilation operators]
[10m] Ladder operators are used to find the energy eigenstates of this system, whose nth energy level equals h-bar omega times n plus one-half.
ANSWER: quantum harmonic oscillator [or QHO; prompt on harmonic oscillator or HO]
[10e] Wick's theorem describes contraction, which is a variation of an operation that shares its name with this property. This mathematical property holds for operators a and b when ab equals ba.
ANSWER: commutativity [or commutes; accept commutator]
<Science - Physics>
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| Adlai E. Stevenson A | Uni of Illinois Laboratory | 0 | 0 | 10 | 10 |
| Audrain County AT | Northview | 0 | 0 | 0 | 0 |
| Belmont | Innovation Academy A | 0 | 0 | 10 | 10 |
| Fremd | Alabama Cyber Tech | 10 | 10 | 10 | 30 |
| Johns Creek | Richard Montgomery | 10 | 10 | 10 | 30 |
| Lambert A | Montgomery Blair A | 0 | 0 | 10 | 10 |
| Lexington | Detroit Catholic Central A | 0 | 10 | 10 | 20 |
| Northmont | Eastchester | 0 | 0 | 10 | 10 |
| Strake Jesuit A | Hunter A | 0 | 0 | 10 | 10 |
| Thomas Jefferson A | Strake Jesuit B | 0 | 10 | 10 | 20 |
| Walter Payton A | Lindbergh | 0 | 0 | 10 | 10 |
| Westwood | Hinsdale Central A | 0 | 0 | 10 | 10 |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2025 PACE NSC | 06/07/2025 | Y | 12 | 14.17 | 92% | 33% | 17% |