Lectures related to Quantum Theory: Canonical Approach

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Quantum Physics II: Operator or Density Matrix

Explores operator, density matrix, subsystems, states, and system evolution in quantum physics.

Scaling & Renormalization in Statistical Mechanics

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Quantum Entanglement

Delves into quantum entanglement, exploring entangled particles' state, evolution, and measurement.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

Compositions and adjoints of unbounded operators

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Ewald Summation: Long-range Interactions and Self-interaction Correction

Explores Ewald summation for long-range interactions and self-interaction correction in Fourier space and real space.

Signal Representation: Fourier Transforms

Covers the representation of signals using Fourier transforms and the properties of signal vectors.

Linear Operators: Quantum Mechanics and Linear Algebra

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Ewald Summation: Electrostatic Coulomb Energy

Explores Ewald summation for electrostatic Coulomb energy in periodic systems, emphasizing the importance of Gaussian screening charges.

Hilbertian Bounded Operators

Introduces Hilbert operators, covering their properties, C*-algebras, and the Fourier transform's unitarity.

Measurement: Quantum State and Observables

Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.

Quantum Theory: Canonical Approach

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

Fourier Analysis: Applications and Inversion Formula

Explores Fourier analysis applications and the inversion formula in the context of periodicity and continuous functions.

Electromagnetic Waves

Covers the theory of electromagnetic waves and provides a detailed understanding of wave propagation.

Quantum Mechanics: Mathematical Framework Log in to Mediaspace to watch this video

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.