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Stone’s theorem gives a one-to-one correspondence between unitary time-evolution operators of isolated quantum systems and operators with this property. For 10 points each:
[10m] Name this property that observables in quantum mechanics are assumed to have since it implies their eigenvalues are real.
ANSWER: self-adjointness [or Hermitianness]
[10h] With Franz Rellich, this physicist gives his name to a theorem stating that perturbations of self-adjoint operators are self-adjoint. A condition named for this Japanese physicist implies electron density isn’t differentiable at the position of the nucleus.
ANSWER: Tosio Kato [accept Kato–Rellich theorem or Kato’s cusp condition or Kato’s theorem]
[10e] The Kato–Rellich theorem is used to show the Hamiltonian is self-adjoint by considering it to be a perturbation of this quantity’s operator. In classical mechanics, this quantity equals momentum squared over twice the mass.
ANSWER: kinetic energy [prompt on energy; prompt on T; prompt on E; prompt on E-sub-k]
<Physics>
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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Columbia AWaterloo A001010E
FloridaLSE1001020ME
Georgia TechChicago B001010E
MITHarvard1001020ME
MinnesotaVirginia Tech1001020ME
North Carolina AIndiana1001020ME
NorthwesternChicago A1001020ME
StanfordIllinois A1001020ME
Toronto ARutgers0101020HE
UC Berkeley AWUSTL A1001020ME
UC Berkeley BNYU001010E
WUSTL BGeorgia State1001020ME

Summary

TournamentExact Match?HeardPPBEasy %Medium %Hard %
2025 ACF NationalsYes1217.50100%67%8%