Jacobs University, Spring 2018
Master programs in Mathematical Physics:
Conferences in Mathematical Physics 2018:
Let me know if you are interested in any of these, then I can give you some more information.
Class:
Wed 15:45 - 17:00, Lecture Hall Research III (until March 21), Lecture Hall Research I (starting April 4)
Fri 14:15 - 15:30, East Hall 4 (until March 16), East Hall 8 (starting March 23)
Syllabus (as of Feb. 1, 2018) available here. (Note that the Syllabus will not be updated, the most recent information can be found on this website.)
This class mainly follows:
Other interesting books are:
See the weekly schedule below for more literature referenced in class.
The final grade is weighted as follows: Homework: 20%, Midterm: 30%, Final: 50%. Students who take both part I and II receive the same grade for part I and II according to the above scheme. For students who take only part I the final grade for part I is weighted 20% homework and 80% midterm.
There will be two exams, a midterm and a final. More details will be announced. Note that this class uses gradescope for grading exams, see here for more information.
Midterm Exam: Fri, Mar. 23, 14:15 - 15:30, East Hall 8
The exam begins at 14:15 sharp, so please come a few minutes earlier to be seated at 14:15. The midterm is about all material up to the Mar. 16 session. You only need to bring a pen, no calculators or notes! Please be aware of the University policy regarding missing exams: Policies for Undergraduate Studies. In particular, in case you are missing an exam due to illness (only with doctor's note) or an emergency, you have to notify me (by email) before the beginning of the exam!
Final Exam: Mon, May 28, 12:30 - 14:30, Lecture Hall Research I
The exam begins at 12:30 sharp, so please come a few minutes earlier to be seated at 12:30. The final exam is about all material from part I and part II of the course, with an emphasis on the material from part II. You only need to bring a pen, no calculators or notes! Please be aware of the University policy regarding missing exams: Policies for Undergraduate Studies. In particular, in case you are missing an exam due to illness (only with doctor's note) or an emergency, you have to notify me (by email) before the beginning of the exam!
Each week on Wednesday (except the first and exam weeks) there will be a homework assignment. These are an integral part of the coursework and working on the exercise sheets consistently is the best preparation for the exams. Note that
| Date | Sheet Number | Due Date |
|---|---|---|
| Feb. 07, 2018 | Sheet 1 | Feb. 16, 2018 (not Feb. 14) |
| Feb. 14, 2018 | Sheet 2 | Feb. 21, 2018 |
| Feb. 21, 2018 | Sheet 3 | Feb. 28, 2018 |
| Feb. 28, 2018 | Sheet 4 | Mar. 07, 2018 |
| Mar. 07, 2018 | Sheet 5 | Mar. 14, 2018 |
| Mar. 14, 2018 | Sheet 6 | Mar. 21, 2018 |
| Mar. 21, 2018 | Sheet 7 | Apr. 04, 2018 |
| Apr. 04, 2018 | Sheet 8 | Apr. 11, 2018 |
| Apr. 11, 2018 | Sheet 9 | Apr. 18, 2018 |
| Apr. 18, 2018 | Sheet 10 | Apr. 25, 2018 |
| Apr. 25, 2018 | Sheet 11 | May 02, 2018 |
| May 02, 2018 | Sheet 12 | May 09, 2018 |
Will be updated while class is progressing.
| Date | Topics |
|---|---|
| Feb. 02, 2018 | Introduction and Overview (double slit, single-particle QM) |
| Feb. 07, 2018 | Introduction and Overview (classical mechanics, many-particle QM, different research topics) Further literature: |
| Feb. 09, 2018 | Fourier transform (free Schrödinger equation, Schwartz functions) |
| Feb. 14, 2018 | Fourier transform (Schwartz space as complete metric space) |
| Feb. 16, 2018 | Fourier transform (properties and inverse, solution to the free Schrödinger equation in the Schwartz space) |
| Feb. 21, 2018 | Fourier transform (pseudo-differential operators, heat equation), tempered distributions |
| Feb. 23, 2018 | Tempered distributions, solution to the free Schrödinger equation for tempered distributions |
| Feb. 28, 2018 | no class (Jacobs Career Fair) |
| Mar. 02, 2018 | Long-time asymptotics of the free Schrödinger equation and the momentum operator (note: guest lecture Prof. Peter Pickl (LMU Munich): Bogoliubov corrections for the Hartree dynamics canceled due to illness) Further literature: |
| Mar. 07, 2018 | Review of Hilbert and Banach spaces (orthogonal basis, separability, Bessel, Cauchy-Schwarz, Parseval) |
| Mar. 09, 2018 | Mean-field dynamics of bosons (replacement for the planned guest lecture last Friday) Further literature: |
| Mar. 14, 2018 | Review of Hilbert and Banach spaces, and bounded linear operators (orthogonal decomposition, operator norm, extension of densely defined bounded linear operators) |
| Mar. 16, 2018 | Unitary groups and their Generators (unitary operators, the free propagator as generator of a unitary group, Sobolev spaces) |
| Mar. 21, 2018 | Unitary groups and their Generators (example of translations); Self-adjoint operators (Riesz representation theorem) |
| Mar. 23, 2018 | Midterm Exam |
| Mar. 28, 2018 | no class (Spring Break) |
| Mar. 30, 2018 | no class (Spring Break) |
| Apr. 04, 2018 | Self-adjoint operators (Riesz representation, Hilbert space adjoint, bounded self-adjoint operators as generators) |
| Apr. 06, 2018 | Self-adjoint operators (unbounded operators and their adjoints, self-adjoint unbounded operators) |
| Apr. 11, 2018 | Self-adjoint operators (graph, closure) |
| Apr. 13, 2018 | Self-adjoint operators (essential self-adjointness, core, criteria for self-adjointness and essential self-adjointness) |
| Apr. 18, 2018 | Self-adjoint operators (examples, deficiency indices, Cayley transform, von Neumann theorem) |
| Apr. 20, 2018 | Self-adjoint operators (resolvent, spectrum, relatively bounded operators, Kato-Rellich) |
| Apr. 25, 2018 | Spectral Theorem (overview about three versions, comparison to finite dimensional case, motivation for functional calculus) |
| Apr. 27, 2018 | Spectral Theorem (Helffer-Sjöstrand formula, almost analytic extensions, functional calculus) |
| May 02, 2018 | guest lecture Prof. Peter Schupp (Jacobs University): Monopoles, Geometry and Algebra |
| May 04, 2018 | guest lecture Prof. Alan Huckleberry (Jacobs University): Random matrices in a bosonic setting |
| May 09, 2018 | Spectral Theorem |
| May 11, 2018 | guest lecture Prof. Alan Huckleberry (Jacobs University): Quotient singularities and measures of entanglement |
| May 16, 2018 | PVMs, POVMs, and measurements |
| May 28, 2018 | Final Exam |