Lectures related to Canonical commutation relation

Canonical Transformations in Analytical Mechanics

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

Canonical Transformations in Hamiltonian Formalism

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

Canonical Equations and Integrable Systems

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

Canonical Transformations: Rules and Equations

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

Canonical Transformations: Symplectic Group and Properties

Explores canonical transformations, symplectic groups, real matrices, preserved quantities, and volumes in phase space.

Gupta-Bleuler Quantization

Covers the Gupta-Bleuler quantization method in Quantum Field Theory, focusing on redundancy in the electromagnetic field and the recovery of Maxwell equations.

Canonical Transformations: Hamiltonian Equations

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

Quantum Physics I

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

Canonical Transformations: Hamilton-Jacobi Equation

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

Quantum Field Theory: Dirac Hamiltonian

Covers the quantization of the Dirac field and its Hamiltonian properties.

Quantum Theory: Canonical Approach

Covers the canonical approach to quantum theory, focusing on Lagrangian mechanics and equations of motion.

Quantum Physics I

Covers the fundamentals of quantum physics, including commutation relations and time evolution operators.

Quantum Field Theory: Heisenberg Representation and Noether Charges

Explores the Heisenberg representation of a free massive real scalar field and the time independence of Noether charges.

Canonical Transformations: Trajectories and Integrable Systems

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

Quantum Harmonic Oscillator: Field Quantization

Explores the quantization of the quantum harmonic oscillator and field, including creation/annihilation operators and the concept of phonons.

Signals & Systems I: Uncertainty Relations and Gaussian Impulse

Explores uncertainty relations, Gaussian impulse, pseudo-probability density, and Gabor functions in signals and systems.

Euclidean Path Integral: Correlation Functions

Explores Euclidean path integrals and correlation functions, showcasing how they relate to real-time correlators.

Quantum Mechanics: Wave Functions and Operators

Explores quantum mechanics, focusing on wave functions, operators, Heisenberg uncertainty principle, and particles in potential wells.

Eigenvalues of Angular Momentum

Explores the eigenvalues of angular momentum operators and their commutation relations.

Canonical Transformations: Phase Portraits and Action Variables

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