Prof. Adrien Bouhon from Nordita will give us a series of lectures in TDLI Meeting Room N499 during Nov. 16-Dec. 2, please see below for more details:

*Modules' contents:

Module A. Conceptual recapitulation of quantum mechanics (study of the one-body Schrödinger equation).

Space of physical wave functions; discrete and continuous orthonormal bases; the square-integrable function space (L^2[R^3]); Hilbert space; non-integrability of continuous bases: the Dirac delta and the plane wave bases; space of continuous linear functionals (dual Hilbert space); Dirac notation: space of generalized quantum states and their representation; the position and momentum operators; first quantization: the Schrödinger equation in the | r > and | k > representations; the Schrödinger equation in an electromagnetic field; principle of gauge invariance in the first quantization.

Module B. Formal aspects of quantum mechanics.

Separability of L^2 and approximation by continuous functions with compact support; Fourier transform and Plancherel’s theorem; (distributions); Sobolev space H^1 and its Fourier characterization; minimization principle of the Schrödinger equation.

Module C. The Schrödinger equation with a periodic potential.

Bravais lattices and the Bloch theorem; Bloch and Wannier bases; band structures; tight-binding models.

Module D. Basic topology & topology of band structures.

The fundamental group of the circle; second homotopy group of the sphere; topology of Bloch vector bundles: Berry phase, Berry connection and Chern number. Chern insulators and Weyl semimetals.

Module E. Crash course in group theory.

The discrete groups and their representations; SO(3) and its (non-projective) representations; electronic orbitals; SU(2) and its projective (spin) representations of SO(3); the irreducible representations (IRREPs) of crystallographic point groups.

Module F. Space groups and their IRREPs & topological classification of band structures with symmetries.

Wyckoff positions; induction of IRREPs; Elementary band representation (EBRs); topology of split EBRs; topological quantum chemistry.

Lecture vedio:
First half of the lecture on 16 November: https://vshare.sjtu.edu.cn/open/789ded3bf5d8ebc1210e0ba799bc3cdf5facaea8b9a1de1688e0c6a4a148e072
Second half of the lecture on 16 November: https://vshare.sjtu.edu.cn/open/b03b045f406e5a27d4c959d20045af39f9ad992c79db0334a81a38f5fd10bfc7
 

Lecture on 17 November: https://vshare.sjtu.edu.cn/open/65f676f37dc3a89cf93cceebde95a89351a56f3b13f122193e7c76f66780433a
Lecture on 20 November:
https://vshare.sjtu.edu.cn/open/b808aebe6aa4bea6707f6e426b032ae6dd5ad6b76a465360f9f27e0e9e5bea4f
Lecture on 24 November:
https://vshare.sjtu.edu.cn/open/095ff46a9d67cae9327833a55fdd340385bb8159411a87629428d121700ade3a