Canonical Transformations in Hamiltonian Formalism

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Canonical Transformations: Rules and Equations

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

Canonical Transformations: Phase Portraits and Action Variables

Explores canonical transformations, phase portraits, and action variables in Hamiltonian systems and harmonic oscillators.

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.

Hamiltonian Mechanics: Analytical Approach

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

Canonical Transformations: Hamiltonian Equations

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

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Canonical Transformations: Hamilton-Jacobi Equation

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

Analytical Mechanics: Lagrange Formalism

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

Quantum Harmonic Oscillator

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