Symplectic geometry & classical mechanics, Problem sheet 4

December 12, 2017

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 4.

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Symplectic geometry & classical mechanics, Problem sheet 3

December 12, 2017

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 3.


Symplectic geometry & classical mechanics, Problem sheet 2

December 12, 2017

For winter semester 2017-18 I am giving a course on symplectic geometry and classical mechanics. This course is intended for anyone with a familiarity with classical mechanics and basic differential geometry. You can find the Youtube playlist here.

Problem sheets are being prepared by Terry Farrelly and will be made available here on my blog, however solutions will *not* be distributed.

Here you can find problem sheet 2.


A QIG seminar on “Approximating Polynomial Optimizations” by David Reeb

June 6, 2016

The quantum information group, Hannover, organises a regular group seminar where members have the opportunity to speak on a variety of themes from communicating early new results, to general interest topics such as reviews of interesting new papers.

In this post I’d like to highlght a video we’ve uploaded of a recent talk by David Reeb on “Approximating Polynomial Optimizations” via semidefinite programs:

If you’d like to see more content like this then please do hit the like button. And if you’d like to keep up to date with content from the quantum information group, Hannover, then please don’t hesitate to subscribe to our channel and my own channel.


Advanced quantum theory

June 6, 2016

This summer semester (2016) I am giving a course on advanced quantum theory. This course is intended for theorists with familiarity with basic textbook single-particle quantum mechanics. The main objective is to understand how to study many interacting particles within QM. We will cover second quantisation, scattering theory, and some elementary relativistic quantum mechanics.

The course is now well under way and there are already several lectures available on youtube in the following playlist. I’ll be posting the rest there as the course develops.

 


The variational principle in quantum mechanics, lectures 9 and 10

June 23, 2011

In lecture 9 we continued reading the papers on matrix product states that we began in lectures 7 and 8.

1. Lecture 10: the time-dependent variational principle

In this lecture we will discuss the time-dependent variation principle (TDVP), which is a powerful method to simulate the nonequilibrium dynamics of a general quantum system while remaining within a given variational class. The TDVP is due, as far as I’m aware, to Dirac. Additionally, describing the TDVP isn’t especially difficult, so it is rather surprising that this elegant method it hasn’t made into standard textbooks. The general framework of the time-dependent variational principle can be found in [P. Kramer and M. Saraceno, Geometry of the Time-Dependent Variational Principle in Quantum Mechanics (Springer-Verlag, Berlin) (1981)].

These notes can be found in pdf format here.

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The variational principle in quantum mechanics, lecture 3

April 25, 2011

1. Lecture 3: The many body problem

In this lecture the many body problem is introduced in the context of first and second quantisation. The lecture notes can also be found here in pdf format.

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