This course on Quantum Theory aims to provide an understanding of the axioms and principles of Quantum Mechanics. Students will learn about Banach Spaces, Separable Hilbert spaces, projectors, bars, kets, measure theory, integration of measurable functions, self-adjoint operators, spectra, perturbation theory, momentum operator, spectral theorems, observables, spin, composite systems, quantum harmonic oscillators, the Fourier Operator, the Schrodinger Operator, and periodic potentials. The course employs a lecture-based teaching method and is designed for individuals interested in gaining a comprehensive knowledge of Quantum Theory.
Overview
Syllabus
Axioms of Quantum Mechanics - Lec01 - Frederic Schuller.
Banach Spaces - Lec02 - Frederic Schuller.
Separable Hilbert spaces - L03 - Frederic Schuller.
Projectors,bars and kets - Lec 04 - Frederic Schuller.
Measure Theory -Lec05- Frederic Schuller.
Integration of measurable functions - Lec06 - Frederic Schuller.
Self adjoint and essentially self-adjoint operators - Lec 07 - Frederic Schuller.
Spectra and perturbation theory - L08 - Frederic Schuller.
Case study: momentum operator - Lec09 - Frederic Schuller.
Inverse Spectral Theorem - L10 - Frederic Schuller.
Spectral Theorem - L11 - Frederic Schuller.
Stone's theorem & construction of observables - L12 - Frederic Schuller.
Spin - L13 - Frederic Schuller.
Composite systems - L14 - Frederic Schuller.
Total spin of composite system - L15 - Frederic Schuller.
Quantum Harmonic Oscillator - L16 - Frederic Schuller.
Quantum Harmonic Oscillator - L17 - Frederic Schuller.
The Fourier Operator - L18 - Frederic Schuller.
The Schrodinger Operator - L19 - Frederic Schuller.
Periodic potentials - L20 - Frederic Schuller.
Periodic potentials - L21 - Frederic Schuller.
Taught by
Frederic Schuller
