Packet P: Bonus 18
Von Neumann (“NOY-mahn”) and Wigner showed that bound states can coexist with a spectrum of eigenstates with this property. For 10 points each:
[10h] Name this property that the position operator has, implying that the position ket space has uncountably infinite dimensions.
ANSWER: continuous [or continuity; or existing in a continuum; accept continuous spectrum; accept bound state in the continuum]
[10e] Every continuous symmetry of the action corresponds to one of these statements, which are often locally expressed as a continuity equation. These statements hold that the total value of a quantity within a physical system is constant.
ANSWER: conservation laws [accept conservation of energy]
[10m] A bound state has a localized wavefunction for which this procedure can be performed on. This procedure cannot be done on position eigenstates since they are not square-integrable.
ANSWER: normalization [or word forms like normalize; accept normalizable; reject “normal”; reject “renormalize” or “renormalization”]
<GC, Physics> | Packet P - Editors 2
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 3 | 23.33 | 67% | 67% | 100% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Harvard A | MIT | 10 | 0 | 10 | 20 | HM |
| Indiana A | Illinois A | 10 | 10 | 0 | 20 | HE |
| Ohio State A | Michigan A | 10 | 10 | 10 | 30 | HEM |