# 15: Advanced Hamiltonian Mechanics

- Page ID
- 9655

- 15.1: Introduction to Advanced Hamiltonian Mechanics
- Hamiltonian mechanics underlies both classical and quantum physics.

- 15.2: Poisson bracket Representation of Hamiltonian Mechanics
- The Poisson bracket representation of Hamiltonian mechanics provides a direct link between classical mechanics and quantum mechanics.

- 15.3: Canonical Transformations in Hamiltonian Mechanics
- Hamiltonian mechanics is an especially elegant and powerful way to derive the equations of motion for complicated systems. Integrating the equations of motion to derive a solution can be a challenge. Hamilton recognized this difficulty, so he proposed using generating functions to make canonical transformations which transform the equations into a known soluble form.

- 15.4: Hamilton-Jacobi Theory
- The Hamilton-Jacobi theory uses a canonical transformation of the Hamiltonian to a solvable form. Relate surfaces of constant action integral to corresponding particle momenta.

- 15.5: Action-angle Variables
- Canonical transformation to action-angle variables provides a solution.

- 15.6: Canonical Perturbation Theory
- Use perturbation theory to solve three-body systems.

- 15.7: Symplectic Representation
- The symplectic representation provides an elegant but appropriate description.

- 15.8: Comparison of the Lagrangian and Hamiltonian Formulations
- Their relative merits.