Lectures on Quantum Theory

This is from a series of lectures - "Lectures on Quantum Theory" delivered by Dr.Frederic P Schuller. Topics covered in this course will include the axioms of quantum mechanics; Hilbert and Banach spaces; projectors, bras and kets; measure theory; integration of measurable functions; self adjoint and essentially self-adjoint operators; spectra and perturbation theory; inverse spectral theorem; spectral theorem; Stone's theorem and construction of observables; spin; composite systems; total spin of a composite system; quantum harmonic oscillator; the Fourier operator; the free Schrodinger operator; and periodic potentials.

Axioms of Quantum Mechanics

Lecture 01 - Axioms of Quantum Mechanics
Lecture 02 - Banach Spaces
Lecture 03 - Separable Hilbert Spaces
Lecture 04 - Projectors, Bras and Kets
Lecture 05 - Measure Theory
Lecture 06 - Integration of Measurable Functions
Lecture 07 - Self Adjoint and Essentially Self-adjoint Operators
Lecture 08 - Spectra and Perturbation Theory
Lecture 09 - Case Study: Momentum Operator
Lecture 10 - Inverse Spectral Theorem
Lecture 11 - Spectral Theorem
Lecture 12 - Stone's Theorem and Construction of Observables
Lecture 13 - Spin
Lecture 14 - Composite Systems
Lecture 15 - Total Spin of a Composite System
Lecture 16 - Quantum Harmonic Oscillator
Lecture 17 - Measurements
Lecture 18 - The Fourier Operator
Lecture 19 - The Free Schrodinger Operator
Lecture 20 - Periodic Potentials
Lecture 21 - Relativistic Quantum Mechanics