Lectures related to Introduction to Quantum Mechanics

Asymptotic States and S-matrix: Operators

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Scattering Theory Overview

Explores scattering theory, S-matrix, T-product, perturbation theory, and Schrödinger equation solutions.

Scattering Amplitude and Green's Functions

Covers the derivation of the scattering amplitude using Lippmann-Schwinger equations and the introduction of Green's functions.

Gauss Representation

Explores the Gauss representation of complex numbers, focusing on addition, multiplication, bases, and vector space dimensions.

Asymptotic States and S-matrix

Explores asymptotic states, S-matrix, Lippmann-Schwinger equation, and energy robustness in quantum field theory.

Relativistic Quantum Mechanics

Introduces relativity into quantum mechanics and discusses the Dirac equation and 4x4 matrices.

Scattering in Quantum Mechanics

Discusses the scattering problem, differential cross-section, total cross-section, and Moller operators in quantum mechanics.

Quantum Scattering: Eigenstates and Amplitudes

Explores quantum scattering, emphasizing eigenstates and amplitudes in the process.

Scattering Amplitude and Optical Theorem

Covers the introduction of scattering amplitude, optical theorem, and unitary operators in quantum mechanics.

Lattices: Properties and Theta Functions

Explores lattices in Rd, Gram matrices, theta functions, and modular properties.

Fourier Series: Harmonic Analysis

Covers the Fourier series representation of periodic signals and harmonic analysis.

Probability and Statistics Log in to Mediaspace to watch this video

Covers mathematical concepts from number theory to probability and statistics.

Singular Value Decomposition: Applications and Interpretation Log in to Mediaspace to watch this video

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Fourier Transform: Concepts and Applications Log in to Mediaspace to watch this video

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Quantum Mechanics: Electron Propagation and Measurement Log in to Mediaspace to watch this video

Covers electron propagation, quantum operators, and the measurement process in quantum mechanics.

Fourier Transform: Basics and Applications Log in to Mediaspace to watch this video

Covers the basics of Fourier transform and the significance of fixed angular momentum states in mass calculations.

Fourier Series: Convergence and Dirichlet Theorem Log in to Mediaspace to watch this video

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Elastic Scattering: Interactions of Electrons with Matter Log in to Mediaspace to watch this video

Covers elastic scattering of fast electrons and their interactions with matter, including the derivation of the Mott formula and effective refractive index.

Quantum Propagation: Hamiltonian and State Decomposition Log in to Mediaspace to watch this video

Discusses quantum propagation, focusing on Hamiltonians, eigenstates, and their time evolution in quantum mechanics.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.