Search result: Catalogue data in Autumn Semester 2022
Mathematics Master  | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
 Application AreaOnly necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area. Credits from other application areas cannot be recognised for further application areas. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Theoretical Physics In the Master's programme in Applied Mathematics 402-0205-00L Quantum Mechanics I is eligible as a course unit in the application area Theoretical Physics, but only if 402-0224-00L Theoretical Physics wasn't or isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Number | Title | Type | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 402-0809-00L | Introduction to Computational Physics | W | 8 credits | 2V + 2U | A. Adelmann | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | This course offers an introduction to computer simulation methods for physics problems and their implementation on PCs and super computers. The covered topics include classical equations of motion, partial differential equations (wave equation, diffusion equation, Maxwell's equations), Monte Carlo simulations, percolation, phase transitions, and N-Body problems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Students learn to apply the following methods: Random number generators, Determination of percolation critical exponents, numerical solution of problems from classical mechanics and electrodynamics, canonical Monte-Carlo simulations to numerically analyze magnetic systems. Students also learn how to implement their own numerical frameworks in Julia and how to use existing libraries to solve physical problems. In addition, students learn to distinguish between different numerical methods to apply them to solve a given physical problem. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Introduction to computer simulation methods for physics problems. Models from classical mechanics, electrodynamics and statistical mechanics as well as some interdisciplinary applications are used to introduce modern programming methods for numerical simulations using Julia. Furthermore, an overview of existing software libraries for numerical simulations is presented. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lecture notes and slides are available online and will be distributed if desired. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Literature recommendations and references are included in the lecture notes. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Lecture and exercise lessons in english, exams in German or in English | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 402-2203-01L | Classical Mechanics | W | 7 credits | 4V + 2U | M. Gaberdiel | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | A conceptual introduction to theoretical physics: Newtonian mechanics, central force problem, oscillations, Lagrangian mechanics, symmetries and conservation laws, Hamiltonian mechanics, canonical transformations, Hamilton-Jacobi equation, spinning top, relativistic space-time structure. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Fundamental understanding of the description of Mechanics in the Lagrangian and Hamiltonian formulation. Detailed understanding of important applications, in particular, the Kepler problem, the physics of rigid bodies (spinning top) and of oscillatory systems. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 402-0861-00L | Statistical Physics | W | 10 credits | 4V + 2U | E. Demler | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | This lecture covers the concepts of classical and quantum statistical physics. Several techniques such as second quantization formalism for fermions, bosons, photons and phonons as well as mean field theory and self-consistent field approximation. These are used to discuss phase transitions, critical phenomena and superfluidity. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | This lecture gives an introduction in the basic concepts and applications of statistical physics for the general use in physics and, in particular, as a preparation for the theoretical solid state physics education. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Kinetic approach to statistical physics: H-theorem, detailed balance and equilibirium conditions. Classical statistical physics: microcanonical ensembles, canonical ensembles and grandcanonical ensembles, applications to simple systems. Quantum statistical physics: density matrix, ensembles, Fermi gas, Bose gas (Bose-Einstein condensation), photons and phonons. Identical quantum particles: many body wave functions, second quantization formalism, equation of motion, correlation functions, selected applications, e.g. Bose-Einstein condensate and coherent state, phonons in elastic media and melting. One-dimensional interacting systems. Phase transitions: mean field approach to Ising model, Gaussian transformation, Ginzburg-Landau theory (Ginzburg criterion), self-consistent field approach, critical phenomena, Peierls' arguments on long-range order. Superfluidity: Quantum liquid Helium: Bogolyubov theory and collective excitations, Gross-Pitaevskii equations, Berezinskii-Kosterlitz-Thouless transition. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Lecture notes available in English. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | No specific book is used for the course. Relevant literature will be given in the course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 402-0843-00L | Quantum Field Theory I Special Students UZH must book the module PHY551 directly at UZH. | W | 10 credits | 4V + 2U | R. Renner | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | This course discusses the quantisation of fields in order to introduce a coherent formalism for the combination of quantum mechanics and special relativity. Topics include: - Relativistic quantum mechanics - Quantisation of bosonic and fermionic fields - Interactions in perturbation theory - Scattering processes and decays - Elementary processes in QED - Radiative corrections | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | The goal of this course is to provide a solid introduction to the formalism, the techniques, and important physical applications of quantum field theory. Furthermore it prepares students for the advanced course in quantum field theory (Quantum Field Theory II), and for work on research projects in theoretical physics, particle physics, and condensed-matter physics. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lecture notes | Will be provided as the course progresses | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Competencies |
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| 402-0830-00L | General Relativity Special Students UZH must book the module PHY511 directly at UZH. | W | 10 credits | 4V + 2U | L. Senatore | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Abstract | Introduction to the theory of general relativity. The course puts a strong focus on the mathematical foundations of the theory as well as the underlying physical principles and concepts. It covers selected applications, such as the Schwarzschild solution and gravitational waves. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Learning objective | Basic understanding of general relativity, its mathematical foundations (in particular the relevant aspects of differential geometry), and some of the phenomena it predicts (with a focus on black holes). | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Content | Introduction to the theory of general relativity. The course puts a strong focus on the mathematical foundations, such as differentiable manifolds, the Riemannian and Lorentzian metric, connections, and curvature. It discusses the underlying physical principles, e.g., the equivalence principle, and concepts, such as curved spacetime and the energy-momentum tensor. The course covers some basic applications and special cases, including the Newtonian limit, post-Newtonian expansions, the Schwarzschild solution, light deflection, and gravitational waves. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literature | Suggested textbooks: C. Misner, K, Thorne and J. Wheeler: Gravitation S. Carroll - Spacetime and Geometry: An Introduction to General Relativity R. Wald - General Relativity S. Weinberg - Gravitation and Cosmology | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| » Electives Theoretical Physics | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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