Summer Term 2026

1300112102
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Content

This course provides a firm understanding of the theoretical concepts of astrophysics, together with their assumptions and limitations. Topics covered include: -- Hydrodynamics: Basics and equations of motion; ideal and viscous fluids and currents; sound waves, supersonic currents and shock waves; instabilities, convection and turbulence -- Plasma physics: Basics of collision-less plasmas; dielectric tensor; dispersion relation, longitudinal waves and Landau damping; magnetohydrodynamic equations; waves in magnetized plasmas; hydrodynamic waves -- Radiative processes: Macroscopic radiation measurements; emission, absorption and scattering, radiative transfer; Bremsstrahlung and synchrotron radiation; ionization and recombination; spectra -- Stellar dynamics: Relaxation; Jeans equations and Jeans theorem; tensor-virial theorem; equilibrium and stability of self-gravitating systems; dynamical friction; Fokker-Planck approximation

Goal

Upon completion of the lecture, students are able to apply this knowledge to a wide range of different areas of modern astrophysics and can solve complex problems in this field. They are familiar with concepts from different areas of theoretical physics relevant for astrophysics and they can apply mathematical techniques for solving questions arising in astrophysical situations.

1300112105
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Content

* Optical telescopes: optics and characteristic parameters, telescope types, diffraction, resolution, aberrations and corrections, applications * Optical detectors: detector types, semiconductors and CCDs, quantum efficiency, readout, noise sources, multi-chip cameras, applications * Imaging: techniques, photometry, data reduction and characterisation, signal-to-noise * Atmospheric effects and corrections: extinction, turbulence, seeing, active and adaptive optics, laser guide stars, applications * Spectroscopy: types of spectrographs and spectrometers, dispersive elements, integral field units, data reduction and characterisation, applications * Infrared astronomy: detectors and techniques, sources, applications * Radio astronomy: detectors and instrumentation, synthesis techniques, types of radiation and sources, applications * Astronomical interferometry: wavelength regimes, instrumentation, applications * X-ray and gamma-ray astronomy: detectors and instrumentation, types of radiation and sources, applications * Astroparticle physics: neutrino and Cherenkov detectors, sources and acceleration mechanisms of neutrinos and cosmic rays, applications * Gravitational-wave astronomy: detection, sources, applications. * In-situ exploration and remote sensing.

Prerequisites

Prerequisites: knowledge of the introductory astronomy lectures (MVAstro0 or WPAstro); basic knowledge of electromagnetic radiation.  Credit points can be acquired either for MVAstro1 or for MKEP5, but not for both modules. The Laboratory Course Astrophysics is recommended as complementary to the MKEP5 module.

Goal

After completing this course, the students have firm insight into the concepts, technologies, and the underlying physical principles and limitations of modern observational techniques along with scientific applications. They have knowledge of basic detector designs for different types of radiation and particles. They understand the environmental influence on astronomical observations. They are able to select and judge the adequate observational technique for studying an astronomical object of interest.

1300142101
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Content

* Structure of solids in real and reciprocal space * Lattice dynamics and phonon band structure * Thermal properties of insulators * Electronic properties of metals and semiconductors: band structure and transport * Optical properties from microwaves to UV * Magnetism * Superconductivity (each chapter includes experimental basics)

Prerequisites

content of PEP1-PEP5, PTP IV (Quantenmechanik)

Goal

After completing the course the students - have gained a thorough understanding of the fundamentals of condensed matter physics and can apply concepts of many-particle quantum mechanics to pose and solve relevant problems. - will be able to describe the priciples of formation of solids and can propose appropriate experimental methods to study structural properties. They are familiar with and can apply the concept of reciprocal space. - they can apply fundamental electronic models to explain and predict properties of crystalline materials as metals, semiconductors, and insulators. - they can ascribe optical, magnetic properties of matter to electronic and structure degrees of freedom. - they can describe and theoretically explain fundamental properties of superconductivity. - they are able to choose appropriate experimental methods for probing structural, optical, magnetic, and electronic properties of condensed matter and can analyse the experimental results.

1300152104
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Content

This lecture introduces all physical concepts of the fundamentals of Environmental Physics and it is accompanied by exercises and tutorials every week. The content spans: ¿ The fundamentals about the Earth climate system and its compartments, flow, transport, and the global radiation balance. ¿ Geophysical fluid dynamics, i.e. the fundamental laws of free and forced fluid movement and vorticity, and a practical guide to the first principles of turbulence. ¿ Global circulation of atmosphere and ocean, boundary layer physics, and slow flow through porous media and of ice. ¿ Gas and heat exchange between ocean and atmosphere. Global fluxes and cycles (energy, water, carbon). ¿ Isotope fractionation and isotope methods to study the Earth environments, focus on water and carbon isotopes. ¿ Introduction to models of environmental systems, basic principles of numerical climate modelling. ¿ Basic principles of radiative transfer. Climate system radiative forcing and sensitivity. Global climate change past, present and future.

Prerequisites

Contents of PEP1-PEP3

Goal

Students achieve a fundamental understanding of the key physical processes and interactions in the Earth surface system and its compartments, as well as of the human impact on these systems and the related societal implications. They are able to solve basic problems of environmental physics and interpret the results in the context of fundamental questions regarding the physics of the earth surface environments and the methodologies to observe and study those.

1300172103
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Content

* Manifolds * Geodetics, curvature, Einstein-Hilbert action * Einstein equations * Cosmology * Differential forms in General Relativity * The Schwarzschild solution * Schwarzschild black holes * More on black holes (Penrose diagrams, charged and rotating black holes) * Unruh effect and hawking radiation

Prerequisites

Contents of PTP1-4

Goal

After completing the course the students * have a thorough knowledge and understanding of Einstein's theory of General Relativity including the necessary tools from differential geometry and applications such as black holes, gravitational radiation and cosmology,  * have acquired the necessary mathematical tools from differential geometry, are trained in their application to physical situations with strong gravity and are familiar with their interpretation, * have advanced competence in the fields of theoretical physics covered by this course, i.e. the ability to analyze physical phenomena using the acquired concepts and techniques, to formulate models and find solutions to specific problems, and to interpret the solutions physically and communicate them efficiently, * are able to broaden their knowledge and competence in this field of theoretical physics on their own by a systematical study of the literature.