Lectures related to Hamiltonian Formalism: Harmonic Oscillator

Quantum Mechanics: Jacobi Identity and Gauge Invariance

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

Canonical Transformations: Hamilton-Jacobi Equation

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

Canonical Transformations: Existence and Equations

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

Canonical Transformations in Analytical Mechanics

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

Hamiltonian Formalism: Conservation Laws

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Canonical Transformations in Hamiltonian Formalism

Explores canonical transformations in Hamiltonian formalism, emphasizing preservation of the action principle and structure necessary for transformations.

Lagrangian Mechanics: Symmetries and Conservation Laws

Explores Lagrangian mechanics, symmetries, conservation laws, and the Hamiltonian concept.

One Dimensional Harmonic Oscillator

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Field Theory: Action Principles

Discusses the application of action principles in classical field theory, focusing on Lagrange and Hamiltonian formulations.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Canonical Transforms: Hamilton-Jacobi Equation

Explores canonical transforms and the Hamilton-Jacobi equation, emphasizing explicit solutions and initial conditions.

Symmetry and Conservation Laws

Explores symmetry, Noether's theorem, and conservation laws in physics, emphasizing the role of time and the Hamiltonian.

Hamilton's Formalism: Equations and Transformations

Explores Hamilton's formalism, canonical equations, and Poisson brackets in classical and quantum mechanics.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Differential Equations: Speed Variation Analysis

Covers the analysis of speed variation using differential equations and small time intervals.

Quantum Mechanics: Path Integral Representation

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

First Order Differential Equation

Covers first-order differential equations, including linear equations and applications in physics.

Variational Calculus and Least Action Principle

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

Differential Equations Solutions

Covers solutions of differential equations with initial conditions and boundedness concepts.