# Search result: Catalogue data in Autumn Semester 2019

Mathematics Master | ||||||

Core Courses For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||

Bachelor Core Courses: Applied Mathematics ... Further restrictions apply, but in particular: 401-3601-00L Probability Theory can only be recognised for the Master Programme if neither 401-3642-00L Brownian Motion and Stochastic Calculus nor 401-3602-00L Applied Stochastic Processes has been recognised for the Bachelor Programme. 402-0205-00L Quantum Mechanics I is eligible as an applied core course, but only if 402-0224-00L Theoretical Physics (offered for the last time in FS 2016) 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 (Link) after having received the credits. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3601-00L | Probability Theory At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. | E- | 10 credits | 4V + 1U | A.‑S. Sznitman | |

Abstract | Basics of probability theory and the theory of stochastic processes in discrete time | |||||

Objective | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||

Content | This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains. | |||||

Lecture notes | available, will be sold in the course | |||||

Literature | R. Durrett, Probability: Theory and examples, Duxbury Press 1996 H. Bauer, Probability Theory, de Gruyter 1996 J. Jacod and P. Protter, Probability essentials, Springer 2004 A. Klenke, Wahrscheinlichkeitstheorie, Springer 2006 D. Williams, Probability with martingales, Cambridge University Press 1991 | |||||

402-0205-00L | Quantum Mechanics I | W | 10 credits | 3V + 2U | G. Blatter | |

Abstract | Introduction to quantum theory: wave mechanics, Schroedinger equation, angular momentum, central force problems, potential scattering, spin. General structure: Hilbert space, states, obervables, equation of motion, density matrix, symmetries, Heisenberg- and interaction picture, approximate methods: perturbation theory, variational approach, quasi-classics. | |||||

Objective | Introduction to single-particle quantum mechanics. Familiarity with basic ideas and concepts (quantisation, operator formalism, symmetries, angular momentum, perturbation theory) and generic examples and applications (bound states, tunneling, hydrogen atom, harmonic oscillator). Ability to solve simple problems. | |||||

Content | Starting from Feynman's path-integral formulation, we develop the operator technique and introduce Dirac's notation. Quantum phenomena are developed by way of example for one-dimensional single particle problems (bound states, tunneling, scattering problems, resonances, periodic and disordered potentials). We introduce rotations and angular momenta and proceed with central symmetric problems, three dimensional scattering theory, spin, and the addition of angular momenta/spin. Various pictures (Schroedinger-, Heisenberg-, Dirac-) are explained and approximative methods such as variational techniques, perturbation theory, and quasi-classical formalism are introduced. | |||||

Lecture notes | Auf Moodle, in deutscher Sprache | |||||

Literature | G. Baim, Lectures on Quantum Mechanics E. Merzbacher, Quantum Mechanics L.I. Schiff, Quantum Mechanics R. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals J.J. Sakurai: Modern Quantum Mechanics A. Messiah: Quantum Mechanics I S. Weinberg: Lectures on Quantum Mechanics |

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