Quantum Mechanics: Basic Principles and Probabilistic Methods

Here is the official site from the department.

Time and place: Tuesday 1-2 in MS.03, Thursday 9-10 in B3.03, and Friday 2-3 in B3.03. Support classes: Monday 11-12 in B1.12. Assessment: 3-hour examination.

Quantum mechanics is one of the most successful and most fundamental scientific theories. It is fundamental in the description of atomic spectra, chemical reactions, electronic properties of condensed matter, superconductivity, etc... This lecture will contain a necessarily brief introduction to some of the fundamental principles of quantum theory: Wave functions in Hilbert space, stationary and time-dependent Schrödinger equations, uncertainty principle, harmonic oscillator and Hydrogen atom (hopefully).

Mathematically, we will use notions of analysis, PDEs, Fourier analysis, functional analysis, algebra, and probability theory. We will review in particular the spectral theorem for unbounded operators and the Feynman-Kac formula. This lecture will be self-contained, although some results will be accepted without proofs.

I occasionally put comments on my facebook page; but anything of importance can also be found here.

Handwritten notes:
Notes, pages 1-4.
Notes, pages 5-8.
Notes, pages 9-12.
Notes, pages 13-16.
Notes, pages 17-20.
Notes, pages 21-24.
Notes, pages 25-28.
Notes, pages 29-32.
Notes, pages 33-36.
Solution to the minimisation problem of p. 36 by K. Matetski, T. Tkocz, R. Toala.
Notes, pages 37-40.
Notes, pages 41-44.
Notes, pages 45-48.
Notes, pages 49-52.
Notes, pages 53-56.
Notes, pages 57-60.
Notes, pages 61-64.
Mathematical complement, pages 1-4.
Mathematical complement, pages 5-8.
Mathematical complement, pages 9-12.