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Many-body Quantum Physics, ESI 2014

by J.P. Solovej

Lectures: Tuesday 4:15-6:15 pm in Schrödinger lecture hall ESI

Exercise class: Thursday 1:00-2:00 pm

Lecture Notes: Notes updated March 5, 2014

Notes on the min-max Theorem base on the Spectral Theorem

Notes on The Lieb Thirring-Inequality

Changes to schedule:

Exercise class Thursday March 13 moved to 9-10
No lectures Tuesday March 18
No Exercise class Thursday March 20
Lectures and Exercise class Friday March 21 9-12
As of April 1 the lectures will be Tuesday 4:15-6:15 pm
On April 8 there will be an additional 90 min lecture. Thus lectures will be from 2:15-4:15 pm. Both lectures will be in the Boltzmann lecture Hall at ESI

Material Covered:

March 11: Chapter 1 in the notes
March 21: Chapter 2, but the proof of Theorem 2.9 will be covered on March 25
March 25: Chapter 3 and 4 up to but not including Theorem 4.12.
April 1: Theorem 4.12 (the Min-Max Principle) (A proof not relying on the spectral theorem is to be found in Appendix C of the notes. A proof based on the spectral theorem is linked above.), Chapter 5. A proof of Theorem 5.10 (The Lieb-Thirring inequality) is linked above.
On April 8 we will begin the discussion of second quantization from Chapter 6,7,8
April 29-May 6: Finished up to Theorem 9.5
May 13: We finish Chapter 9 and start Chapter 10

Exercises:

If somebody wants to volunteer discussing exercises they are more than welcome. If anybody needs credit for the course it is a requirement to be active in exercise class.

March 13: We discussed exercises to Chapter 1 as well as the Young symmetrizer projections.
March 21: We discussed Exercise A.1.2
March 27: We will discuss some of the exercises: 1.25-26, 2.4-7.
April 3: We will do Problem 5.8, 5.12 (and also that V₊ in L^3/2(R³) is sufficient to ensure that the Schrödinger operator is bounded from below.
May 8: Exercise A9.2 and Appendix C

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