Dive deep into the foundations of quantum mechanics through this comprehensive lecture series. Explore key concepts including axioms of quantum mechanics, Banach spaces, Hilbert spaces, and measure theory. Progress to advanced topics such as self-adjoint operators, spectral theory, and perturbation theory. Examine practical applications with case studies on momentum operators, spin systems, and composite systems. Delve into the quantum harmonic oscillator, Fourier operators, and Schrödinger operators. Conclude with an in-depth look at periodic potentials. Gain a thorough understanding of quantum theory from Professor Frederic Schuller over 21 lectures, providing a solid mathematical foundation for further study in quantum physics.
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
