# Quantum state: Quiz

Question 1: In a more general mathematical context, quantum states can be understood as positive normalized linear functionals on a ________; see GNS construction.
Von Neumann algebraMatrix (mathematics)C*-algebraHilbert space

Question 2: Doing this, we determine the initial position q and the initial ________ p of the particle.
MomentumEnergyForceClassical mechanics

Question 3: The observables P(t) and Q(t) will produce random results now; they become ________, and their values in a single measurement cannot be predicted.
Random variableVarianceProbability distributionProbability

Question 4: The ________ state is a superposition of two different states, one of which corresponds to the photon having passed through the left slit, and the other corresponding to passage through the right slit.
PhotonElectronStandard ModelAtom

Question 5: A mixed quantum state is a ________ of pure states (see quantum statistical mechanics).
EntropyPartition function (statistical mechanics)Canonical ensembleStatistical ensemble (mathematical physics)

Question 6: In ________, a quantum state is a mathematical object that fully describes a quantum system.
Introduction to quantum mechanicsWave–particle dualitySchrödinger equationQuantum mechanics

Question 7: As with any vector space, if a basis is chosen for the Hilbert space of a system, then any ket can be expanded as a ________ of those basis elements.
Euclidean vectorLinear combinationInner product spaceDual space

Question 8: For a mathematical discussion on states as functionals, see ________.
Hilbert spaceGelfand–Naimark–Segal constructionC*-algebraCauchy–Schwarz inequality

Question 9: In physics, ________ is often used to denote such vectors.
Bra-ket notationQuantum mechanicsSchrödinger equationQuantum state

Question 10: [4] Another, equivalent, criterion is that the ________ is 0 for a pure state, and strictly positive for a mixed state.
Quantum statistical mechanicsVon Neumann entropyQuantum entanglementDensity matrix