Canonical Transformations: Hamilton-Jacobi Equation

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Canonical Transformations: Rules and Equations

Explores canonical transformations, rules, equations, gauge invariance, and the principle of least action.

Analytical Mechanics: Lagrange Formalism

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Hamiltonian Mechanics: Analytical Approach

Explores Hamiltonian mechanics, conservation laws, potential functions, and canonical transformations in analytical detail.

Material Point Model: Basics

Covers the material point model, initial conditions, and Newton's laws in physics.

Harmonic Oscillator

Explores the harmonic oscillator, covering energy functions, equations of motion, and operator constructions.

Canonical Equations and Integrable Systems

Explores canonical equations, integrable systems, trajectories, and the symplectic matrix in understanding system dynamics.

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

Canonical Transformations: Hamiltonian Equations

Explores canonical transformations, emphasizing Hamiltonian equations, constant quantities, and the importance of Lagrangian variables.

Canonical Transformations: Properties and Applications

Explores canonical transformations, their properties, and applications in Hamiltonian mechanics, emphasizing their role in simplifying the analysis of complex systems.

Harmonic Oscillator: Algebraic Approach

Explores the classical harmonic oscillator and its algebraic approach to studying the system.