Kommentare Sommersemester 2025
Veranstaltungsbeschreibungen in Deutsch und für englisch-sprachige Master-Veranstatungen in Englisch. Course descriptions in German and for Master courses in English.
Mathematik I für Studierende der Physik
Dozent: Prof. Dr. Heidi Rzehak
Zeit: 4 st., Mo 14-16, Mi 10-12
Ort: HS I
9 ECTS
Start: 23.04.2025
ILIAS
Programm:
- Topologien im Rn
- Ableitung (mehrkomponentiger) Funktionen, auch in mehreren Variablen, Ableitungsregeln
- Taylor-Entwicklung
- Gewöhnliche Differentialgleichungen
- Koordinatensysteme, speziell Polar-, Zylinder- und Kugelkoordinaten
- Integration (mehrkomponentig), Wegintegration, Flächen- und Volumenintegration, Gauß‘scher und Stokes’scher Satz
- Symmetrische Bilinearformen: Orthogonalbasen, Sylvester'scher Trägheitssatz
- Euklidische und Hermitesche Vektorräume: Skalarprodukte, Kreuzprodukt, Gram'sche Determinante
- Gram-Schmidt-Verfahren, orthogonale Transformationen, (selbst-) adjungierte Abbildungen, Spektralsatz, Hauptachsentransformation
- Affine Räume
- Fourier Analyse
- Distributionen
Vorkenntnisse:
Inhalte der Grundvorlesungen Analysis I und Lineare Algebra I
Einführende Literatur:
Experimentalphysik II (Elektromagnetismus und Optik)
Dozent: Prof. Dr. Oliver Waldmann
Zeit: 4 st., Di, Do 10-12,
Ort: Großer HS
Fragestunde: Mi 12-14, HS I
8 ECTS
Start: 22.04.2025
ILIAS
Programm:
Die Vorlesung Experimentalphysik II vermittelt die experimentellen Grundlagen der Elektrizität, des Magnetismus und der Optik. Im Zentrum der Vorlesung stehen Demonstrationsexperimente. Die Vorlesung wird durch Übungen begleitet.
Folgende Themen werden behandelt:
- Elektrische Ladung
- Elektrische Felder
- Gaußscher Satz und elektrisches Potential
- Kapazität
- Elektrischer Strom, Widerstand und Stromkreise
- Magnetfelder
- Strominduzierte Magnetfelder, Induktion und Induktivität
- Wechselstrom und Schwingkreise
- Maxwellgleichungen und elektromagnetische Wellen
- Geometrische Optik
- Reflexion und Brechung von Licht
- Licht als Welle: Interferenz und Beugung
Vorkenntnisse:
Experimentalphysik I
Einführende Literatur:
- W. Demtröder, Experimentalphysik 2, Elektrizität und Optik, Springer-Verlag
- Tipler / Mosca, Physik, Springer Verlag
- J. Heintze, Lehrbuch der Experimentalphysik, Band 3: Elektrizität und Magnetismus, Springer Verlag
- Bergmann / Schäfer, Lehrbuch der Experimentalphysik, Band 2, Elektromagnetismus, Verlag de Gruyter
Experimentalphysik IV (Atom-, Molekül- und Festkörperphysik)
Dozent: apl. Prof. Dr. Bernd von Issendorff
Zeit: 4 st., Mi, Fr 10-12
Ort: Großer HS
7 ECTS
Start: 23.04.2025
ILIAS
Programm:
- Komplexe atomare Systeme und periodisches System
- Struktur und Eigenschaften von Molekülen
- Struktur und Eigenschaften von Festkörpern und Oberflächen
Vorkenntnisse:
Experimentalphysik I-III
Einführende Literatur:
Theoretische Physik I (Mechanik und Spezielle Relativitätstheorie)
Dozent: Prof. Dr. Gerhard Stock
Zeit: 4 st., Mo 10-12, Do 12-14
Ort: HS I
9 ECTS
Start: 24.04.2025
ILIAS
Programm:
- Mechanik des Punktteilchens
- Systeme von Massenpunkten
- Bewegung in Zentralkraftfeldern
- Inertialsysteme und beschleunigte Bezugssysteme
- Symmetrien, Invarianzen und Erhaltungsgrößen
- Methode der Lagrange-Multiplikatoren
- Hamiltonsches Prinzip
- Lineare Schwingungen
- Hamilton-Mechanik
- Dynamik starrer Körper
- Spezielle Relativitätstheorie
Vorkenntnisse:
Theoretische Physik I
Einführende Literatur:
- V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer
- H. Goldstein, C.P. Poole, J.L. Safko, Klassische Mechanik, Wiley-VCH
- J. Honerkamp, H. Römer, Grundlagen der Klassischen Theoretischen Physik, Springer
- F. Kuypers, Klassische Mechanik, Wiley-VCH
- L.D. Landau, E.M. Lifshitz, Lehrbuch der Theoretischen Physik, Band I, Akademie-Verlag
- W. Nolting, Grundkurs Theoretische Physik, Band 1, 2 und 4, Springer
- H. Römer, M. Forger, Elementare Feldtheorie, VCH
Theoretische Physik III (Quantenmechanik)
Dozent: Prof. Dr. Jens Timmer
Zeit: 4 st., Di 12-14, Do 10-12
Ort: HS I
8 ECTS
Start: 22.04.2025
ILIAS
Programm:
- Schrödingergleichung
- Eindimensionale Probleme
- Wasserstoffatom
- Spin
- Drehimplus
- Störungstheorie
- ...
- EPR -Paradoxon und Bell'sche Ungleichungen
Vorkenntnisse:
Theoretische Physik I-II, Analysis und Lineare Algebra
Einführende Literatur:
- F. Schwabl. Quantenmechanik
- T. Fließbach. Quantenmechanik
Experimentelle Methoden
Dozent: Prof. Dr. Brian Moser
Zeit: 2 st., Di 10-12
Ort: HS I
Start: 22.04.2025
ILIAS
Programm:
- Statistische Methoden der Datenanalyse
- Computergestützte Datenanalyse
- Grundlagen der Elektronik
- Digitale und analoge Messtechnik
- Grundlagen von Detektoren
Hinweis:
Die erfolgreiche Teilnahme an dieser Veranstaltung ist Voraussetzung zur Teilnahme am Physiklabor für Fortgeschrittene.
Seminar Physik: tba
Dozenten: NN
Zeit: 2 st,
Ort:
4 ECTS
Themen:
Seminar Physik: tba
Dozenten: NN
Zeit: 2 st,
4 ECTS
Themen (vorläufig):
Seminar Physik: tba
Dozenten: NN
Zeit: 2 st,
Ort:
4 ECTS
Themen:
Einführung in Mathematica
Dozent: PD Dr. Maximilian Stahlhofen
Zeit: 2 st., Mo, Mi 14-16
Ort: CIP II
Übungen: 1 st.
5 ECTS
Start: 23.04.2025
Programm:
Wolfram Mathematica ist eine leistungsstarke höhere Programmiersprache, die aktiv in der aktuellen Forschung verwendet wird. Sie verfügt über umfassende Funktionalität im Bereich von symbolischen sowie numerischen Berechnungen. Der Fokus der Vorlesung liegt auf dem Lösen von physikalischen Problemstellungen mit Hilfe von Mathematica. Die Vorlesung gliedert sich grob in zwei Teile.
Im ersten Teil wird das Mathematica Notebook Interface und häufig genutzte Funkionen vorgestellt:
- Eingabe von Ausdrücken in das interaktive Notebook
- Algebraische Manipulationen (z.B. Faktorisierung)
- Differentiation, Integration, Reihenentwicklung
- Lineare Algebra - Plotten
- Differentialgleichungen
Der zweite Teil behandelt mehr den Aspekt von Mathematica als höhere Programmiersprache:
- Prozedurale Programmierung (Schleifen, Bedingungen, …)
- Listen, Associations,
- Strukturerkennung (pattern matching)
- Funktionale Programmierung
Vorkenntnisse:
Theoretische Physik I und II. Die Theoretische Physik III sollte erfolgreich bestanden sein oder im selben Semester gehört werden.
Einführende Literatur:
Einführung in die Moderne Digitalelektronik
Dozent: apl. Prof. Dr. Horst Fischer
Zeit: 2 st., Mo-Fr 10-12
Ort: SR I
Übungen: Mo-Fr 14-17, CIP Pool II
7 ECTS
Blockkurs: ?.07.-?.08.2025
Programm:
Die Teilnehmenden erhalten einen Überblick über die wesentlichen Anwendungsgebiete und Methoden in der heutigen Digitalelektronik. Sie lernen an Hand von Beispielen die Konzepte und Funktionsweise digitaler Schaltkreise kennen und werden in die Programmierung von logischen Bausteinen eingeführt. In der praktischen Übung werden Logikbausteine (FPGA) selbst programmiert.
Folgende Themen werden behandelt:
- Anwendungsfelder der Digitalelektronik
- Grundlagen und logische Verknüpfungen
- Schaltkreisfamilien
- Rechenschaltungen
- programmierbare Bausteine (FPGA und CPLD)
- Zahlen und Speicher
- Automaten
- Systeme zur Datenaufzeichnung
Vorkenntnisse:
Einführende Literatur:
- Urbansk, Digitaltechnik (Springer)
- Tietze Schenk, Halbleitertechnik (Springer)
Hydrodynamik
Dozent: Prof. Dr. Antonio Ferriz-Mas (Universidad de Vigo und Inst. für Sonnenphysik, KIS)
Zeit: Mo 14-16, Mi 12-14, 3 st.
Ort: SR II/III
Übungen: Do oder Fr 12-14, SR II/III
7 ECTS
Start: Voraussichtlich Anfang Mai
Vorlesungs-Programm (pdf)
Programm:
Dieser Kurs bietet einen kompakten und (hoffentlich) klaren Überblick über das Gebiet der klassischen Hydrodynamik. Es wird versucht, einen Mittelweg zwischen den Abstraktionen der reinen Mathematik und dem Empirismus der Ingenieurwissenschaften zu finden.
Im ersten Block gibt es 9 Pflichtthemen, die die zentrale Achse des Faches bilden und die grundlegenden Prinzipien der Hydrodynamik darstellen. Aus Zeitgründen können wir nicht auf die wichtigen Themen der Stabilität und der Turbulenz eingehen. In einem zweiten Block werden 3 Wahlthemen angeboten, aus denen die Studenten eines (oder maximal zwei, je nach verfügbarer Zeit) auswählen können.
- Kinematik des Kontinuums. Euler’sche und Lagrange’sche Darstellungen.
- Kräfte in der Kontinuumsmechanik.
- Grundgleichungen der Kontinuumsmechanik.
- Newton’sche Fluide.
- Energiegleichung für Newton’sche Fluide.
- Zirkulation und Vortizität.
- Inkompressible viskose Strömungen.
- Schallwellen in einem homogenen Medium.
- Die hydrodynamischen Gleichungen in Erhaltungsform.
- Wahlthema: Rotierende Flüssigkeiten.
- Wahlthema: Der Virialsatz und astrophysikalische Anwendungen.
- Wahlthema: Einführung in die Magnetohydrodynamik.
Vorkenntnisse:
Die Vorlesung richtet sich an Studenten/innen der Physik oder der (angewandten) Mathematik. Grundkenntnisse in Thermodynamik wären wünschenswert. Solide Grundkenntnisse in Differential- und Integralrechnung sind erforderlich. Die Studenten sollten mindestens eine Vorlesung in klassischer Mechanik gehört haben (Theoretische Physik I).
Literatur:
- Elementary Fluid Dynamics. D. J. Acheson, Oxford University Press (1990).
- An introduction to fluid mechanics. G. K. Batchelor, Cambridge University Press (1970)
- Course of Theoretical Physics (Vol. VI: Fluid Mechanics). L. D. Landau & E. M. Lifschitz, Pergamon Press Ltd. (1959)
- A First Course in Fluid Dynamics. A. R. Paterson, Cambridge University Press (1983)
- The Navier-Stokes equations: A classifications of flows and exact solutions. Norman Riley & Philip Drazin, London Mathematical Society Lecture Notes Series 334, Cambridge University Press (2006, 2007)
- Physical fluid dynamics. D. J. Tritton, Oxford Science Publications. [2nd edition 1988]
- Theoretical fluid dynamics. Bhimsen K. Shivamoggi, serie Mechanics of fluids and transport processes, Martinus Nijhoff Publishers, Dordrecht, [2d edition 1998].
- The Physics of Fluids and Plasmas: An Introduction for Astrophysicists. A. R. Choudhuri, Cambridge University Press (1998, 2012). ISBN-10: 0762106913
Vorkurs Einführung in Programmieren mit Python
Dozent: Dr. Michael Böhler
Zeit: Blockveranstaltung ganztägig, Vorlesungsbeginn: Mi 9.04 - Fr. 11.04.2025
Vorlesung: täglich 9-12
Übungen: nachmittags 13-16
1 ECTS im BOK-Bereich
Ort: SR II/III
Start: 09.04.2025
ILIAS
Der Vorkurs findet unter Einhaltung der Hygiene- und Abstandsregelungen in Präsenz im Hörsaal I der Physik statt. Der Kurs ist ganztägig und besteht aus Vorlesung und Programmierübungen.
Registrieren Sie sich bitte für den Kurs auf https://ilias.uni-freiburg.de/goto.php?target=crs_3384079&client_id=unifreiburg ("Vorkurs Einführung in Programmieren mit Python des Physikalischen Instituts").
Programm:
Vermittlung von Programmiergrundkenntnisse:
Grundideen der Softwareentwicklung, Variablen, Funktionen, Schleifen, einfache Datentypen (Strings, Tuples, Listen, Dictionaries), Umgang mit Dateien, Modulen, Exceptions und Grundlagen der Objektorientierten Programmierung
Vorkenntnisse:
keine
Einführende Literatur:
Sonnenobservatorium und Astrophysik auf dem Schauinsland - Exkursion im Physik Lehramtsstudium
Dozenten:
Dr. Andreas Härtel (andreas.haertel@physik.uni-freiburg.de),
Dr. Rolf Schlichenmaier (schliche@leibniz-kis.de)
Termin: (*) 16.5. auf 17.5. oder 23.5. auf 24.5. oder 4.7. auf 5.7. oder 11.7. auf 12.7. (Vorbesprechung am 23.4. um 16:15 Uhr)
(*) Die Exkursion findet am ersten der drei Termine statt, an welchem das Wetter geeignet ist.
Ort: Observatorium Schauinsland
ILIAS
Wir treffen uns am Freitag um 15 Uhr am Sonnenobservatorium auf dem Schauinsland. Nach einer Einführung Nutzen wir Spektrographen und Teleskope zum Studium unserer Sonne und in der Nacht zur Beobachtung entfernter Sterne und Galaxien. Die Veranstaltung endet am Samstag Vormittag.
- Beobachtung von Sonnensprektrum und -flecken
- Spektroskopie von Doppelsternen
- Beobachtung von Nebeln und Galaxien
- Austausch und Grillen unter den Sternen
Kompakte Fortgeschrittene Theoretische Physik
Dozent: PD Dr. Steffen Wolf
Zeit: 4 st., Di, Do 14-16
Ort: SR I
7 ECTS
Start: 22.04.2025
ILIAS
Programm:
Diese Vorlesung gehört für Studierende im polyvalenten 2-HF-Bachelor zu den Pflichtveranstaltungen. Abweichend von der Prüfungsordnung wird die Teilnahme im 4. Fachsemester empfohlen, sofern die Theoretische Physik I und II erfolgreich absolviert wurden. Der inhaltliche Schwerpunkt dieser Vorlesung liegt auf der Quantenmechanik, allerdings bezieht sich ein Teil des Inhalts auch auf die Theoretische Thermodynamik und die Statistische Mechanik. Soweit es im Rahmen dieser Vorlesung möglich ist, wird bezüglich der Themenauswahl auf die Bedürfnisse der zukünftigen Lehrkräfte eingegangen. Außerdem werden an entsprechenden Stellen mögliche Elementarisierungen aufgezeigt, die sich für den Schulunterricht anbieten. Nach der aktuellen Prüfungsordnung findet am Ende der Vorlesung eine Klausur statt, die benotet wird und als Prüfungsleistung zählt. Parallel zur Vorlesung finden Übungen statt, deren Teilnahme dringend empfohlen wird. Außerdem sollten rund 50 Prozent der Hausaufgaben richtig bearbeitet sein.
Vorkenntnisse:
Theoretische Physik I und II
Literatur:
- "Quantenmechanik (nicht nur) für Lehramtsstudierende", T. Filk, Springer-Verlag 2019; als E-Book für Mitglieder der Universität Freiburg frei erhältlich
Ausgewählte Kapitel der modernen Physik
Dozent: apl. Prof. Dr. Thomas Filk
Zeit: 2 st., Do 16-18
Ort: HS II
Übungen: 2 st. n.V.
5 ECTS
Start: 24.04.2025
ILIAS
Programm:
Diese Vorlesung richtet sich in erster Linie an Lehramtsstudierende der Physik. Sie kann als Wahlpflichtvorlesung im Master of Education gehört werden oder auch im Bachelor als Spezialvorlesung, falls Mathematik das zweite Hauptfach ist. Inhaltlich deckt diese Vorlesung einige Themen ab, die im normalen Curriculum nicht oder nur am Rande behandelt werden, die aber für zukünftige Lehrer*Innen relevant sind, entweder weil sie im Rahmenlehrplan der Oberstufe vorgesehen sind oder aber zur Motivation der Schüler*Innen beitragen können.
Programm (Auswahl):
- Standardmodell der Kosmologie
- elementare Einführung in die Allgemeine Relativitätstheorie
- elementare Einführung in die Astrophysik
- Halbleiter und Photovoltaik, etc.
- Bildgebende Verfahren in der Medizin
- Physik des Klimas
Vorkenntnisse:
Man sollte die Exp I-III sowie die Theo I und II erfolgreich gehört haben. Begleittexte zur Vorlesung findet man auf der Webseite der Physikdidaktik: www.physikdidaktik.uni-freiburg.de/kurztexte/
Fachdidaktik 2: Diagnostizieren und Fördern im sprachsensiblen Physikunterricht
Dozent: JProf. Dr. Martin Schwichow, Nadja Wulff
(Veranstaltung der Pädagogischen Hochschule)
Zeit: Mo 14:15-15:45
Ort: Pädagogische Hochschule KG 3-111
Start: 28.04.2025
Link-LSF PH
Um sich anzumelden, erscheinen Sie bitte persönlich zur ersten Sitzung am 17.04.2023. Um an dem Kurs teilzunehmen und auf das PH ILIAS zuzugreifen, benötigen Sie einen PH Account. Bitte beantragen Sie den Account rechtzeitig vor Semesterbeginn. Hier wird beschrieben, wie sie diesen beantragen können:
https://www.face-freiburg.de/studium-lehre/im-studium/uni-lv-finden/
Die Veranstaltung wird nur im Sommersemester angeboten. Studierende, welche noch nicht die Veranstaltung Fachdidaktik 1 besucht haben, können trotzdem an dieser Veranstaltung teilnehmen.
Fachdidaktik der Physik der Kursstufe (Didaktik der Modernen Physik)
Dozent: apl. Prof. Dr. Thomas Filk
Zeit: Do 14-16
Ort: HS II
Start: 24.04.2025
Dieses Seminar richtet sich an Studierende im M.Ed.
Theoretical Condensed Matter Physics
Lecturer: Prof. Dr. Tanja Schilling
Time: 4 + 2 st., Mi 12-14, Do 10-12
Room: HS II
Tutorials: n.V.
9 ECTS
Start: 23.04.2025
ILIAS
Program:
- Interactions and phase transitions
- Structure of solids and liquids
- Density Functional Theory
- Soft and charged condensed Matter
- Linear response theory
Prerequisits:
Theoretical Physics I-IV
Literature:
- C. Kittel, "Introduction to Solid State Physics"
- J.P. Hansen, I.R. McDonald, "Theory of Simple Liquids"
- P. Chaikin, T. Lubensky, "Principles of Condensed Matter Physics"
Complex Quantum Systems
Lecturer: apl Prof. Dr. Heinz-Peter Breuer
Time: 4 + 2 st., Di 12-14, Do 14-16
Room: SR II/III
Tutorials: n.V.
9 ECTS
Start: 22.04.2025
Program:
- Quantum mechanical principles
- Density operator formulation
- Dynamics of quantum systems
- Composite quantum systems
- Open quantum systems
- Quantum transport
Prerequisites: Advanced Quantum Mechanics
Literature:
- H.-P. Breuer and F. Petruccione, "The Theory of Open Quantum Systems"
- U. Weiss, "Quantum Dissipative Systems"
- E. Fick, G. Sauermann, "The Quantum Statistics of Dynamic Processes"
- J. Audretsch, "Entangled Systems"
- D.J. Tannor, "Introduction to Quantum Mechanics: A Time-Dependent Perspective"
- H. Kleinert, "Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets"
- M. Di Ventra, "Electrical Transport in Nanoscale Systems"
Introduction to Relativistic Quantum Field Theory
Lecturer: Prof. Dr. Stefan Dittmaier
Time: 4 st., Di 12-14, Mi 10-12
Room: HS II
Tutorials: Mi 14-16, HS II
Start: 22.04.2025
Weblink
ILIAS
Program:
- Quantization of scalar fields (Klein Gordon equation, classical field theory, canonical quantization, scattering theory and Feynman diagrams)
- Vector-boson fields (classical field equations, electromagnetic interactions and the gauge principle, quantization of the electromagnetic field, scalar QED and perturbative evaluation)
- Dirac fermions (basics of Lie Groups, Lorentz group and its representations, Dirac and Weyl equations, Poincare group and its representations, quantization of free Dirac fields, QED and perturbative evaluation, applications)
- Quantization with functional integrals
Prerequisits:
Quantum Mechanics, Electrodynamics and Special Relativity
Literature:
- Bjorken, Drell: "Relativistic Quantum Mechanics"
- Bjorken, Drell: "Relativistic Quantum Fields"
- Itzykson, Zuber: "Quantum Field Theory"
- Maggiore: "A Modern Introduction to Quantum Field Theory"
- Peskin, Schroeder: "An Introduction to Quantum Field Theory"
- Schwartz, "Quantum Field Theory and the Standard Model"
- Sterman: "An Introduction to Quantum Field Theory"
- Srednicki: "Quantum field theory"
- Tung: "Group Theory in Physics"
- Weinberg: "The Quantum Theory of Fields, Vol.1: Foundations"
Computational Physics: Materials Science
Lecturer: Prof. Dr. Joachim Dzubiella
Time: 4 h, Di, Do 10-12
Room: SR Westbau 2.OG
Tutorials: 2 h, n.V.
9 ECTS
Start: 22.04.2025
ILIAS
Program:
Application of computational simulation methods can help to discover or design new materials and investigate (microscopic) structure- (macroscopic) property relationships of a wide range of materials classes, such as metals, composites, nanostructures, electrolyte solvents, as well as polymers, surfactants, or colloidal dispersions. This course will introduce basic statistical concepts as well as programming and simulations techniques with particular focus on methods based on classical Hamiltonians spanning orders of length and time scales, such as Molecular Dynamics and coarse-grained Brownian Dynamics simulations. The students will become familiar with some examples for the different types of interatomic and coarse-grained potentials: e.g., Lennard-Jones, (screened) Coulomb, Hamaker, etc., as well as bonded potentials for molecules and polymers. The course will consist of lectures and hands-on programming exercises and small projects, simulating mostly (interacting) fluids and molecules, using own written code.
Criteria for passing:
For successfully qualifying for the Studienleistung (SL), students must complete, at least an average of 50% of the exercises and attend the tutorials regularly and actively (including the presentation of results). The Prüfungsleistung (PL) consists of a final project or a written exam.
Prerequisits:
Basic knowledge in programming (Python, C/C++) as well as statistical mechanics and thermodynamics.
Literature:
- Script (will be available via ILIAS)
- Book: Understanding molecular simulation from algorithms to applications. D. Frenkel and B. Smit. AP Academic Press.
- Book: Computer simulation of liquids. M. P. Allen and D. J. Tildesley. Oxford University Press. 3rd edition (2017)
Advanced Optics and Lasers
Lecturer: Dr. Kirk Madison
Time: 4 + 2 st., Do 10-12, Fr 14-16
Room: SR GMH
9 ECTS
Start: 24.04.2025
ILIAS
Program:
In this course, we will discuss the principles of lasers and their application. We will start with the fundamentals of light-matter interaction and the basic principles of lasers. We will continue with a discussion of various laser types, ranging from narrow-bandwidth continuous wave lasers used for high-resolution spectroscopy, to ultrashort-pulsed lasers used to study nonlinear physics and light-induced dynamics on the nano- to femtosecond timescale. We will then discuss nonlinear optical phenomena such as nonlinear wavelength mixing, parametric conversion and their application in modern laser systems. Eventually, we will have an outlook on very recent laser developments. Examples are high harmonic generation, Free Electron Lasers or frequency combs.
The lecture will focus on experimental and some basic theoretical principles. The tutorials include problem sheets as well as practical exercises on different laser systems in our lab.
Summary of topics:
- Light-matter interaction
- Coherence and interference
- The laser principle
- Optical resonators
- Gaussian beam optics
- Ultra-short laser pulses
- Nonlinear optics and parametric amplification
- Recent laser developments
Prerequisits:
Experimental Physics I-IV
Literature:
- W. Lange “Laserphysik”
- Demtröder “Laserspektroskopie”
- J. Eichler & H.J. Eichler, Springer, „Laser“
- F.K. Kneubühl /M.W. Sigrist “Laser”
- D. Meschede “Optik, Licht und Laser”
- C. Ruilliere, Springer, "Femtosecond laser pulses“
Condensed Matter II: Interfaces and Nanostructures
Dozent: Prof. Dr. Günter Reiter
Zeit: 4 st., Do, Fr 8-10
Ort: HS II
9 ECTS
Start: 24.04.2025
ILIAS
Program:
The students should get an overview over phenomena which only appear on surfaces and interfaces (e.g. how to make water running uphill?). The course deals with special structural and electronic properties of liquid and solid surfaces as well as their relevance in many fields of modern material science and nanotechnology.
Surfaces between solids and liquids can be found in most of the physical, chemical, biological and geological systems, as well as in many technological processes. Although the number of atoms or molecules at these surfaces is comparatively small, this "minority" can often dominate or even control the behavior of large (macroscopic) systems.
Topics:
- General description of interfaces: Thermodynamics and kinetics
- Interaction forces at interfaces: Short- and long range forces, ...
- Liquids and liquid interfaces: Droplets, bubbles, waves, "liquid beads"
- Solid-liquid interfaces: Hydrodynamics, capillarity, wetting, ...
- Structure of solid surfaces: Electronic processes at surfaces
- Surface processes: Adsorption/desorption, phase transitions
- Making of well defined solid surfaces: Surface reconstruction, surface transport, ...
- Growth- and decay: Epitaxy, nucleation, lattice mismatches, mechanical stress
- Organic layers and nanostructures on surfaces: Directed stucturing of surfaces at nm-scale
Prerequisits:
Experimentalphysik IV (Condensed Matter)
Literature:
- Intermolecular and Surface Forces, With Applications to Colloidal and Biological Systems, Jacob Israelachvili, Academic Press 1995 bzw. Elsevier 2008
- "Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves" von P.-G. de Gennes, F. Brochard-Wyart und D. Quéré, Springer, New York, 2004
- John A. Venables, Lecture notes on Surfaces and Thin Films
- I. Markov, Crystal Growth for Beginners, World Scientific
Hadron Collider Physics
Lecturer: Prof. Dr. Markus Schumacher
Time: 4 st., Mo, Di 10-12
Room: SR GMH
Tutorials:
9 ECTS
Start: 22.04.2025
ILIAS
Program:
In this lecture Physics at Hadron Colliders is discussed. The focus lies on the discussion of recent physics measurements performed at the Large Hadron Collider (LHC) at CERN. They include experimental tests of the Standard Model, Higgs boson physics and searches for extensions of the Standard Model.
The Program consists of:
- Lectures (4h per week)
- Exercises / tutorials (2 h per week), including computer simulations and analysis of ATLAS physics events
Topics:
- Accelerators
- LHC detectors
- Phenomenology of pp collisions
- Structure functions, cross sections
- Particle signatures in LHC experiments
- Inelastic pp collisions
- Production of jets, test of perturbative QCD
- Physics of W and Z bosons
- The top quark and its properties
- Search for the Higgs boson, measurements of the properties of the new particle at 126 GeV
- Search for supersymmetric particles
- Search for other extensions of the Standard Model
Prerequisits:
Experimental Physics V (Nuclear and Particle Physics)
Particle Physics II (desirable)
Literature:
- F. Halzen, A.D. Martin, Quarks and Leptons, Wiley-Verlag;
- D. Griffiths, Introduction to Elementary Particles, Wiley-Verlag;
- G. Kane, A. Price (Ed.), Perspectives on LHC Physics, World Scientific;
- R.K. Ellis, W.J. Stirling und B.R. Webber, QCD and Collider Physics, Cambridge Univ. press;
- D. Green, High PT Physics at Hadron Colliders, Cambridge Univ. press;
- J.M. Campbell, J.W. Huston und W.J. Stirling, Hard interactions of quarks and gluons: a primer for LHC physics, Rep. Prog. Phys. 70 (2007) 89-193.
Astroparticle Physics
Lecturer: Prof. Dr. Marc Schumann
Time: 4 st., Do, Fr 10-12
Room: SR I
9 ECTS
Start: 24.04.2025
Program:
- The standard model of particle physics
- Conservation Rules and symmetries
- The expanding universe
- Matter, Radiation
- Dark matter
- Dark energy
- Development of structure in the early universe
- Particle physics in the stars
- Nature and sources of high energy cosmic particles
- Gamma ray and neutrino astronomy
Prerequisits:
Experimentalphysik V (Kern- und Teilchenphysik)
Literature:
- Perkins: Particle Astrophysics (Oxford)
- Grupen: Astroparticle Physics (Springer)
- de Angelis: Introduction to Particle and Astroparticle Physics (Springer)
- Bergstrom: Cosmology and Astroparticle Physics (Springer)
- Perkins: Introduction to High Energy Physics (Addison-Wesley)
- Barr et al.: Particle Physics in the LHC era (Oxford)
- Bertone (ed): Particle Dark Matter (Cambridge)
- Bartelmann: Das kosmologische Standardmodell (Springer)
- Kolanoski, Wermes: Particle Detectors (Oxford)
- Leo: Techniques for Nuclear and Particle Physics Experiments (Springer)
Quantum Information Theory
Dozent: Dr. Gabriel Dufour, Prof. Dr. Andreas Buchleitner
Time: 4 st. Mo, Di 10-12
Room: HS II
Tutorials: Do 16-18, SR I
9 ECTS
Start: 22.04.2025
Program:
Certain information processing tasks can be performed more efficiently with quantum mechanical than with classical systems. Famous examples are Shor's quantum algorithm for factoring large integer numbers and quantum cryptography enabling secure communication between two parties. In this lecture, we will introduce fundamental concepts of quantum information theory (e.g. entangled states and quantum correlations) and discuss possible applications such as quantum teleportation or quantum computing.
- Foundations of quantum information theory
(Quantum state space, qubits, composite systems, tensor product, correlations and entanglement, quantum entropies)
- Quantum cryptography
(Quantum key distribution, BB84 protocol)
- Quantum computation
(Quantum gates, quantum circuit model, universal quantum gates, quantum algorithms: Shor, Grover)
- Physical realizations
(Trapped ions, cavities, NMR, squids, spintronics)
- Quantum error correction
(Quantum noise, quantum operations, quantum error correction, fault-tolerant quantum computation)
Prerequisits:
Theoretical Physics I-IV (B.Sc. Physik)
Literature:
Quantum Hardware
Dozent: Prof. Dr. Tobias Schaetz
Zeit: 4 st., Mo 14-16, Mi 16-18
Ort: SR GMH
Übungen: n.V.
9 ECTS
Start: 23.04.2025
ILIAS
Program:
- Introduction (qubit concept; entanglement)
- Quantum platforms: photons, cold atoms, ions, spins, SQUID
- Quantum sensing
- Potential applications: quantum computing; quantum simulations; cryptography
Prerequisits:
Experimental Physics I-IV (B.Sc. Physik)
Literature:
Special Relativity
Dozent: Jun.-Prof. Dr. Simone Biondini
Zeit: 2 st., Mi 12-14
Ort: SR I
Tutorials: Di 16-18 (bi-weekly)
5 ECTS
Start: 23.04.2025
Programme:
This course explores one of the most groundbreaking theories in modern physics, formulated by Albert Einstein in 1905. Special relativity revolutionized our understanding of space, time, and motion, challenging classical Newtonian mechanics and introducing concepts such as time dilation, length contraction, and the equivalence of mass and energy.
Throughout this course, we will analyse the experimental foundations of Special Relativity, develop its mathematical framework, and explore its profound implications for physics. We will learn about relativistic kinematics and look at electromagnetism with new eyes.
A solid grasp of classical mechanics and basic electromagnetism will be helpful as we delve into these fascinating ideas.
Get ready to rethink your intuition about time and space.
Preliminaries/Previous knowledge:
The course is addressed to last year bachelor students, as well as master students as elective subject.
Literature:
- Anthony P. French "Special Relativity"
Multi-junction solar cell technology and concentrator photovolatic
Dozent: Prof. Dr. Andreas Bett
Zeit: 2 st., Mo 14-16
Ort: SR I
3 ECTS
Start: 28.04.2025
ILIAS
Programme:
- multi-junction solar cell approach to increase the sunlight conversion efficiency, different solar cell architectures/li>
- introduction III-V materials, adjustment of band-gap, growth techniques/li>
- methods for charaterisation of III-V materials and multi-junction solar cells/li>
- PV concentrator technology: low and high concentration/li>
- componentes of CPV systems: optics, cells, manufacturing/li>
- CPV system analysis including an economical evalution
Preliminaries/Previous knowledge:
Literature:
- "Solar Cells and Their Applications", L. Fraas, L.Partain, Wiley, 2010;
- "Advanced Concetps in Photovoltaics", AJ Nozik, G. Conibeer, MC Beard, Royal Society of Chemistry, 2014;
- "Next Generation Photovoltaics", AB Cristobal Lopez, A. Marti Vega, A. Luque Lopez, Springer Series in Optical Sciences 165, 2012,
- "Concentrator Phtovoltaics", A Luque, V. Andreev, Springer Verlag, Series in Optical Sciences, 2011
Flavour Physics
Dozent: Prof. Dr. Marco Gersabeck
Zeit: 3 st., Mo 13-16
Ort: HS II
7 ECTS
Start: 28.04.2025
Programme:
- Introduction: particles and symmetries
- Quark flavour physics: mixing and CP violation, (semi-)leptonic decays, rare decays
- Charged lepton flavour physics
- Neutrino physics: scattering, production and detection, oscillations, masses, CP violation
- Electric dipole moment experiments
Prerequisites:
Experimentalphysik V, Kern- und Teilchenphysik. Advanced Particle Physics (recommended).
Literature:
- M. Sozzi: Discrete Symmetries, Oxford University Press
- A.A. Petrov: Indirect Searches for New Physics, CRC Press
- M. Thomson: Modern Particle Physics, Cambridge University Press
- Y. Grossman and Y. Nir: The Standard Model, Princeton University Press
Numerical recipes for physicists
Dozent: Jun.-Prof. Dr. Stefan Vogl
Zeit: 3 st., Mo 12-14
Ort: SR I
5 ECTS
Übungen: Do 16-18, CIP II
Start: 28.04.2025
Course-Link
Programme:
Only highly idealized problems can be solved analytically. The solution to all realistic problems rely on numerical methods and their implementation on a computer. This course introduces some of the most important numerical methods and their application in physics.
- Errors and uncertainties
- Integration
- Differentiation
- Root finding
- Ordinary differential equations
- Partial differential equations
Preliminaries/Previous knowledge:
None beyond the requirements for the Master’s program in Physics, basic programming skills and interest in problem solving with a computer helpful
Literature:
- R. Landau: "Computational physics", Wiley-VCH, 2007
Quantum Transport
Dozent:PD Dr. Michael Walter
Zeit: Fr 14-16
Ort: SR II/III
Start: 25.04.2025
Übung: 14-tägig, 2-st
Programme:
Transport properties are highly relevant for many technological applications like electronics (transport of electrons) or solar cells (separation of positive and negative charge carriers generated by light). In contrast to classical flow or diffusion, quantum properties -- such as the wave nature of a quantum particle, tunneling or the quantization of energy levels -- become relevant on microscopic scales and make quantum transport different from classical transport governed by Newton's equations.
In this lecture, I will present an explicit description of an electronic device at the atomic scale, with the aim to arrive at a single molecule transistor, which is very likely to be the basis of future electronics. The system is completely characterized and the energy levels of contacts and the isolated molecule are known. We develop the formalism to describe the conductance of such a device during the course.
Preliminary Program:
- Atomistic view of conductance (energy levels, quantum of conductance)
- Basis functions and band structure (basis functions, tight-binding, subbands)
- Hopping, Marcus description
- Density matrix, Green function, spectral functions
- Open systems (level broadening, lifetime)
- Coherent transport (transmission, Landau-Büttiker formalism)
- Non-coherent transport and Ohm's law
Prerequisits:
Theoretical Physics III (Quantum Mechanics)
Literature:
- S. Datta, Quantum Transport: Atom to Transistor (Cambridge University Press, Cambridge, England, 2005).
Theory and Modeling of Materials: Superconductivity II (Microscopic Theory)
Lecturer: apl Prof. Dr. Christian Elsässer
Time: 2 + 1 st., Fr 8-10
Room: SR I
5 ECTS
Start: 02.05.2025
Exercises: approx. bi-weekly 2 hours on appointment (1 SWS)
ECTS points: 3 (three) for succesful participation in lectures only; 3+2 (five) for attendance of lectures, participation in exercises, and final oral exam.
Program:
In Superconductivity I (WS 2024/25), the phenomenology of superconductivity has been addressed.
- Fundamental experiments: persistent current, perfect diamagnetism, isotope effect, flux quantization.
- Type-I and Type-II superconductivity.
- Phenomenological theories: London, Ginzburg-Landau, Lawrence-Doniach.
- Characteristic parameters: critical temperature T_c, critical fields and currents, penetration depth, coherence length.
In Superconductivity II (SS 2025), microscopic theories of superconductivity will be addressed.
- Introduction to the quantum mechanics of homogeneous superconductors; Cooper's problem.
- Electron-phonon interaction in normal metals and superconductors.
- Theory of Bardeen, Cooper and Schrieffer; the energy gap; experimental observations.
- Thermal and optical excitations; derivation of thermodynamic properties.
- Quantum mechanics of inhomogeneous superconductors.
Textbooks, e.g.:
- M. Tinkham, Introduction to Superconductivity
- W. Buckel, R. Kleiner, Superconductivity: Fundamentals and Applications
- J. R. Schrieffer, Theory of Superconductivity
- A. L. Fetter, J. D. Walecka, Quantum Theory of Many-Particle Systems
Cellular Self-Organization and Molecular Machines
Dozent: Prof. Dr. Thorsten Hugel (Inst. of Physical Chemistry), Dr. Thomas Pfohl
Zeit: 2 + 1 st., Fr 10-12
Ort: SR GMH
Übungen: Do 8-9, SR GMH
5 ECTS
Start: 25.04.2025
Program:
- Fundamental forces in Nano-Biosystems (elastic, viscous, thermal, chemical, entropic, polymerization)
- Concepts of equilibrium and non-equilibrium systems and measurements
- Jarzynski equation
- Linear and rotational molecular motors
- Molecular details of muscle function
- Optical and magnetic tweezers, AFM
- Single molecule force spectroscopy
- Single molecule fluorescence
- Concepts of nanotribology and biolubrication
Prerequisits:
Basic knowledge of statistics and optics is helpful but not mandatory.
Literature:
- Jonathon Howard: “Mechanics of Motor Proteins and the Cytoskeleton“ (2005)
- Phil Nelson: "Biological Physics: Energy, Information, Life" (2003)
- Rob Philips, Jane Kondev, Julie Theriot, Hernan Garcia: "Physical Biology of the Cell" (2012)
- Recent journal publications
Laser-based Spectroscopy and Analytical Methods
Dozent: PD Dr. Frank Kühnemann (Fraunhofer IPM)
Zeit: 2 + 1 st., Di 14-17
Ort: SR GMH
5 ECTS
Start: 22.04.2025
Program:
Lasers did become a powerful tool for measurement applications in areas like industry, medicine, or environment. The current course focuses on the use of tuneable lasers to interrogate the spectral “fingerprints” of gases, liquids and solids for analytical purposes. Typical examples are air quality monitoring or process control in industry.
The lecture block in the first half of the course will give a comprehensive introduction into the following topics
- Infrared molecular spectra
- Tuneable lasers
- Spectroscopic techniques (absorption, photoacoustic spectroscopy, cavity-based methods)
- Background signals, noise and detection limits
The seminar talks in the second block will focus on the application of different spectroscopic methods for analytical tasks. At the start of the course, students will choose from a list of provided topics to prepare a talk and a short written summary. The preparation will be supported by topical literature and discussion sessions with the course staff. Duration of the talks will be appr. 30 minutes, followed by a discussion of content and presentation style.
Prerequisits:
Advanced Optics and Lasers (recommended)
Literature:
Nano-Photonics – Optical Manipulation and Particle Dynamics
Dozent: Prof. Dr. Alexander Rohrbach
Zeit: 3 st., Di 14-16:30
Ort: SR II/III
7 ECTS
Start: 22.04.2025
ILIAS
Motivation:
You think basic physics research and applied research leading to a social benefit cannot be well combined? When particles or macro-molecules undergo thermal collisions with smaller molecules in (complex) fluids or in air, thermal (Brownian) motion with stochastic changes in positions and velocities take place - beyond our imagination. Such particles can be viruses or particulates from combustion engines in the air that get into contact with e.g. lung cells. How can a limited number of photons be generated in such a way that they scatter efficiently at the small, fast particles and carry the maximum information with them. How can the particle information encoded by the scattered photons be amplified by intelligent detection mechanisms? How can rare but important interaction events be manipulated by photon momentum transfer and optical forces?
In this lecture you will learn
- the transfer from the Maxwell equations and the electromagnetic force density to optical forces and optical tweezers, which allow to control molecular processes relevant to cellular biology and medicine
- the basics of light scattering, how photons transfer momentum to microscopic objects and how scattered photons transfer information about the state of the objects. In contrast to incoherent photons, coherent light encodes significantly more information about small objects, which, driven by thermal forces, continuously change their position and orientation relative to their environment. All this can be directly measured through µs-nm particle tracking.
- how smallest probes can interact on a molecular scale with their environment, which can be analyzed by correlations of changes in the probe’s states. In this way, the interactions of probes with living cells give new insights into cellular diseases, such as bacterial and viral infections, but also exposure of particulate matter to lung cells.
The summer term lecture “Wave Optics” is quite helpful to hear, but not mandatory.
Contents
- Introduction
- Light – Carrier of Information and Actor
- Microscopy und Light Focussing
- Light Scattering
- Manipulation by Optical Forces
- Particle Tracking beyond the Uncertainty Regime
- Thermal Motion and Calibration
- Photonic Force Microscopy
- Applications in Biophysics and Medicine
- Time-Multiplexing and holographic optical traps
- Applications in Micro- and Nano-Technology
- Appendix
Wave Optics
Dozent: Prof. Dr. Alexander Rohrbach
Zeit: 3 st., Mi 13-16
Ort: SR 01-012, G.-Köhler-Allee 102, IMTEK
7 ECTS
Start: 23.04.2025
ILIAS
We do not really know what light is, although the concepts to describe light as waves or as particles usually work well. It is a nontrivial task to explain the colorful intensity distributions we see every day, i.e. the interactions of light with matter. Controlling light on the macroscale and the nanoscale is the key for generating impact in research, development and industry. However, this requires a thorough understanding of wave optics and its powerful theoretical instrument, the description by Fourier transforms.
This english lecture is accompanied by many live experiments and by weekly tutorials, where exercises are discussed that students have to calculate from one week to the next.
The new lecture is a fusion of the two former lectures “Moderne Optik I & II“ and is now organized in 6 chapters.
1. Introduction
Some motivation, literature and a bit of history
2. From Electromagnetic Theory to Optics
What is light ? Which illustrative pictures do the Maxwell equations provide? If matter, dielectric and metallic, consists of coupled, damped springs (harmonic oscillators), how does matter depend on the frequency of light ? What do the wave equation and the Helmholtz equation express and how can one handle waves in position space and frequency space.
3. Fourier-Optics
How does a wave transforms position information into directional information ? Why can this be well described by Fourier transformations in 1D, 2D and 3D ? What has this to do with linear optical system theory including spatial frequency filters and the sampling theorem?
4. Wave-optical Light Propagation and Diffraction
Different methods are introduced of how to describe the propagation of ways in position space and frequency space. We do the direct transfer from propagation to diffraction of light and momentum space. We treat evanescent waves, thin diffracted objects, the propagation of light in inhomogeneous media and the diffraction at gratings. This allows to discuss important active elements such as acousto-optic and spatial light modulators. We end with adaptive optics and phase conjugation.
5. Interference, Coherence and Holography
We learn how a composition of k-vectors define the phases of interfering waves and the resulting stripe patterns. The relative phases of each partial wave in space and time change the interference significantly and define the coherence of light - these concepts will be discussed in detail. We learn how to write and read phase information in holography.
6. Light Scattering and Plasmonics
The interaction of light with matter is based on particle scattering: we discuss the theoretical concepts of light scattering on the background of Fourier theory. We expend these approaches to photon diffusion, nonlinear optics, fluorescence and Raman scattering or scattering at semiconductor quantum dots - which are all hot topics in modern Photonics. A big emphasis is put on the description of surface plasmons and particle plasmons, where light can be extremely confined.
1. Introduction
1.1. Motivation
1.2. Literatur
1.3. A bit of history
2. From Electromagnetic Theory to Optics
2.1. What is Light?
2.2. The Maxwell-equations
2.3. The change of Light in Matter
2.4. Wave equation and Helmholtz equation
2.5. Waves in position space and frequency space
3. Fourier-Optics
3.1. Introduction
3.2. The Fourier-Transformation
3.3. Linear Optical Systems
3.4. Spatial frequency filters
3.5. The Sampling Theorem
4. Wave-optical Light Propagation and Diffraction
4.1. Paraxial light propagation by Gaussian beams
4.2. Wave Propagation and Diffraction
4.3. Evanescent waves
4.4. Diffraction at thin Phase and Amplitude Objects
4.5. Light Propagation in inhomogeneous Media
4.6. Diffraction at gratings
4.7. Acousto Optics
4.8. Spatial Light Modulators
4.9. Adaptive Optics and Phase Conjugation
5. Interference, coherence and holography
5.1. Some Basics
5.2. Interferometry
5.3. Foundations of Coherence Theory
5.4. Principles of Holography
6. Light Scattering and Plasmonics
5.5. Scattering of light at particles
5.6. Photon Diffusion
5.7. Basics of Nonlinear Optics
5.8. Fluorescence und Raman-scattering
Theoretical Astrophysics: Stellar Structure and Evolution
Lecturer: Dr. Petri Käpylä, Dr. Ivan Milic (Inst. für Sonnenphysik, KIS)
Time: 2 + 1 st., Di 14-16
Room: SR WB 2.OG
Tutorials: Fr 16-18, SR WB 2.OG
5 ECTS
Start:
Program:
- Equations of stellar structure and energy generation and transport in stars
- Stellar evolution
- Stellar atmospheres
- The Sun among stars: dynamo, activity, interior structure and solar spectroscopy
Literature:
- Dina Prialnik “An introduction to the theory of stellar structure and evolution”, Cambridge University Press
- Frank Shu “Physics of Astrophysics I and II”, University Science Books
- Rob Rutten, “Radiative Transfer in Stellar Atmospheres”
Astronomisches Praktikum
Dozent: Dr. Rolf Schlichenmaier, Dr. Juan Borrero
Zeit: 4 st., Kompaktkurs Ende Juli / Anfang August
Vorbesprechung: tba
Bei Interesse bitte eine kurze Anmeldung bis 20.04.2024 per e-mail an rolf.schlichenmaier@leibniz-kis.de
Termin: n.V.
Ort: Schauinsland-Observatorium des KIS
Maximale Teilnehmerzahl: 5
Veranstaltungs link
Programm:
Das Astronomische Praktikum findet als Kompaktkurs statt, zu Beginn der vorlesungsfreien Zeit. Alle Versuche werden im Observation Schauinsland des KIS durchgeführt.
Das Programm umfasst
- Bestimmung der Magnetfeldstärke in Sonnenflecken
- Messung der Sonnenrotationsgeschwindigkeit
- Bildrekonstruktionsverfahren
- Photometrie von Sternhaufen
- Einführung in die digitale Datenverarbeitung
Die Anleitungen sind auf der Vorlesungsseite des KIS abrufbar.
Vorkenntnisse:
Vorlesung "Einführung in die Astrophysik"
Einführende Literatur:
Unsöld & Baschek: Der neue Kosmos
Term Paper: Current Questions in Particle Physics
Lecturer: Prof. Dr. Marco Gersabeck
Time: Do 13-14
Room: HS II
6 ECTS
Program:
Term Paper: tba
Lecturer: NN
Time:
Room:
6 ECTS
Program:
Term Paper: tba
Lecturer: NN
Time:
Room:
6 ECTS
Program: