Packet 1: Bonus 6
This operator’s components are the prototypical spherical basis in 3-dimensional space. For 10 points each:
[10e] Name this operator whose total amount is conserved in rotationally invariant systems by Noether’s theorem. In quantum physics, this operator is divided into “orbital” and “intrinsic” forms.
ANSWER: angular momentum [accept L or J; accept total angular momentum or orbital angular momentum or intrinsic angular momentum; reject “momentum”]
[10m] Addition of angular momenta is readily done by a basis change from a space where the summands have this property to one where the sum does. Matrices commute if and only if they have the “simultaneous” form of this property.
ANSWER: diagonalizable [or diagonalizability; accept simultaneously diagonalizable; reject “diagonal”]
[10h] For two spin-half particles, the basis change produces a space made by performing this operation to a spin-1 and spin-0 space. A Fock space is made by performing this operation on a sequence of n-particle Hilbert spaces.
ANSWER: direct sum [prompt on sum]
<Editors, Physics> | J. Playoffs 1 (Editors 1)
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 24 | 11.25 | 71% | 29% | 13% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| British Columbia | Georgia Tech C | 0 | 0 | 0 | 0 | |
| Bruin | Ohio State | 0 | 0 | 0 | 0 | |
| Chicago B | Swarthmore | 10 | 10 | 0 | 20 | EM |
| Columbia A | Northwestern A | 10 | 0 | 0 | 10 | E |
| Cornell | Brown | 10 | 10 | 0 | 20 | EM |
| Georgetown | Northwestern B | 0 | 0 | 0 | 0 | |
| Georgia Tech A | Stanford B | 0 | 0 | 0 | 0 | |
| Harvard | Stanford A | 10 | 0 | 0 | 10 | E |
| Johns Hopkins | NYU B | 10 | 0 | 10 | 20 | EH |
| MIT | UCLA | 10 | 10 | 10 | 30 | EMH |
| Minnesota | Cambridge | 0 | 0 | 0 | 0 | |
| NYU A | Maryland A | 0 | 0 | 0 | 0 | |
| North Carolina | Maryland B | 0 | 10 | 0 | 10 | M |
| Penn State | Columbia B | 10 | 0 | 0 | 10 | E |
| Pittsburgh | Illinois A | 10 | 0 | 0 | 10 | E |
| Rutgers | Michigan | 10 | 10 | 0 | 20 | EM |
| Toronto B | Texas | 10 | 0 | 0 | 10 | E |
| UC Berkeley A | Toronto A | 10 | 10 | 10 | 30 | EMH |
| UC Berkeley B | Chicago A | 10 | 0 | 0 | 10 | E |
| UCF | Illinois B | 10 | 0 | 0 | 10 | E |
| Virginia | Georgia Tech B | 10 | 0 | 0 | 10 | E |
| Virginia Tech | Indiana | 10 | 0 | 0 | 10 | E |
| WashU | Vanderbilt | 10 | 10 | 0 | 20 | EM |
| Waterloo | Purdue | 10 | 0 | 0 | 10 | E |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| Main Site | 2026-04-17 | ✓ | 24 | 11.25 | 71% | 29% | 13% |