M8 · Hamilton-Jacobi theory
A 21-module path through m8 · hamilton-jacobi theory, in study order from foundations to the frontier.
Modules
- Hamilton-Jacobi Equation
- Hamilton's Principal Function
- Generating Function to a Trivial Hamiltonian
- Hamilton's Characteristic Function
- Time-Independent Hamilton-Jacobi Equation
- Separation of Variables in Hamilton-Jacobi Theory
- Staeckel Conditions for Separability
- Action-Angle Variables
- Action Integrals over Invariant Tori
- Frequencies from Action-Angle Variables
- Liouville Integrable Systems
- Liouville-Arnold Theorem
- Degeneracy and Commensurate Frequencies
- Adiabatic Invariants
- Adiabatic Theorem for Slowly Varying Hamiltonians
- Hannay's Angle
- Old Quantum Theory and Bohr-Sommerfeld Quantization
- WKB Approximation and the Eikonal Connection
- Optical-Mechanical Analogy
- Connection to the Schrodinger Equation
- Canonical Perturbation Theory