# Hamiltonian mechanics: Quiz

Question 1: An interesting and promising area of research is the study of ________, where an infinite number of independent conserved quantities can be constructed.
Poisson bracketIntegrable systemAction-angle coordinatesHamilton–Jacobi equation

Question 2: (Force equals the negative ________ of potential energy.)

Question 3: The Poisson bracket gives the space of functions on the manifold the structure of a ________.
Special unitary groupLie algebra representationLie groupLie algebra

Question 4: Hamilton's equations are appealing in view of their beautiful simplicity and (slightly broken) ________.
SymmetryEuclidean groupGroup (mathematics)Symmetry (physics)

Question 5: For a detailed derivation of these equations from ________, see below.
ForceHamiltonian mechanicsClassical mechanicsLagrangian mechanics

Question 6: There is a set of ________ known as the Hamilton equations which give the time evolution of the system.
CalculusDynamical systems theoryDifferential equationMathematics

Question 7: A Hamiltonian system may be understood as a ________ E over time R, with the fibers Et, tR being the position space.
Principal bundleFiber bundleDifferentiable manifoldManifold

Question 8: Any smooth real-valued function H on a ________ can be used to define a Hamiltonian system.
Hamiltonian mechanicsSymplectic manifoldDifferentiable manifoldCotangent bundle

Question 9: Every ________ G over the symplectic manifold generates a one-parameter family of symplectomorphisms and if { G, H } = 0, then G is conserved and the symplectomorphisms are symmetry transformations.
Smooth functionDerivativeFunction (mathematics)Differentiable manifold

Question 10: The Hamilton's equations above work well for ________, but not for quantum mechanics, since the differential equations discussed assume that one can specify the exact position and momentum of the particle simultaneously at any point in time.
ForceEnergyPhysicsClassical mechanics