Canonical Transformations: Properties and Applications

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Explores charged particles in a magnetic field, focusing on Landau levels and gauge transformations.

Explores discrete and continuous degrees of freedom, canonical commutation relations, and the correspondence between classical and quantum mechanics.

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Explores canonical equations for isolated systems, finding solutions and analyzing impulses.

Covers canonical transformations and the Hamilton-Jacobi equation, emphasizing explicit motion solutions and system evolution.

Covers the verification of single qubit Hamiltonians using various techniques and methods.

Explores the classical dynamics and quantization of a harmonic LC oscillator.

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.

Explores classical and quantum physics concepts related to the interaction with an external electromagnetic field.

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