Canonical Transformations: Rules and Equations

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Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Covers the path integral representation in quantum mechanics and the dynamics of systems described by Lagrangian.

Explores trajectories in integrable systems and the challenges of making predictions.

Explores Hamiltonian and Lagrangian formulations, canonical variables, Lie operators, and their applications in beam dynamics and nonlinear systems.

Explores particle accelerator dynamics, transfer maps, Hamiltonian equations, and phase space conservation.

Explores the Hamiltonian of an atom in a magnetic field and its paramagnetic and diamagnetic responses.

Explores phase space, the Poisson bracket, and Hamiltonian mechanics concepts.

Explores the behavior of charged particles in magnetic fields and the invariance of quantum probabilities.

Covers the principle of least action and variational calculus in discovering equations of motion.

Covers classical mechanics, including Newton's, Lagrange's, and Hamilton's formulations for calculating particle positions over time.