German Research School for Simulation Sciences and RWTH Aachen University

WS 2017/18, Thu 09:30-12:00 and 13:15-15:45, Lecture Hall, GRS Jülich (RWTHonline)

WS 2017/18, Thu 09:30-12:00 and 13:15-15:45, Lecture Hall, GRS Jülich (RWTHonline)

Do not forget to **register** for the exam.

### Lectures

Erik Koch

The **final exam** will be on Thu, 14 Februrary 2019 from 09:30 to 12:00 in the GRS Lecture Hall, Jülich.

**Why Quantum Mechanics?**

Particle-waves and Schrödinger equation

Particle in a box

slides and exercises

links to movies etc.:**time-dependent Schrödinger equation**

probability interpretation and continuity equation

separation of variables and time-independent Schrödinger equation

initial value problem (Crank-Nicolson vs. eigenstate expansion)

Gaussian wave packets (animation)

slides and exercises**piece-wise constant potentials**

matching of wave functions

potential step, tunneling

finite potential well (example: 20 Å wide, 4 eV deep; read off*k*in Å)_{n}

slides and exercises**linear potentials and numerical solution of the Schrödinger equation**

linear potential and dimensionless units

Airy functions (NIST Digital Library of Mathematical Functions)

asymptotics of wave functions

numerical solution: finite differences and Numerov trick

stability of integration

slides and exercises**harmonic oscillator**

analytic solution, Hermite polynomials

algebraic solution, ladder operators

slides and exercises**formalism of quantum mechanics**

measurement and expectation value

Dirac notation, inner product, Hilbert space

linear operators, inverse, unitary, Hermitian

slides and exercises**common eigenfunctions of commuting operators**

simultaneous diagonalization of operators

uncertainty relations

slides and exercises**spherical symmetry and angular momentum**

spherical coordinates

radial Schödinger equation

angular momentum algebra

slides and exercises**spherical harmonics**

calculating spherical harmonics

interactive visualization and how it is done: tutorial (zip)

slides and exercises**Xmas Lecture: Quantum Computing**

IBM Quantum Experience: Web access to IBM toy quantum computer

slides and tutorial (zip)**hydrogen atom**

radial equation

analytic solution, Laguerre polynomials

atomic orbitals, periodic table

self-consistent calculations for many-electron systems

slides and exercises

interactive page for calculating many-electron atoms**perturbation theory**

first and second order, non-degenerate and degenerate

slides and exercises**time-dependent perturbation theory**

first order; harmonic perturbation, Fermi's golden rule

slides and exercises**basis sets and tight-binding**

chemical bonds: covalent, polar, ionic

Born-Oppenheimer approximation

Hellmann-Feynman theorem

slides- overview of lectures in the SiSc physics track

Erik Koch