Details
Lecture notes:
Thomas Fermi and Hartree Fock theories
[ last update: May, 28 2014 ]
Exercise class notes
1. Hardy-Littlewood-Sobolev and Young inequalities
(lecture notes, adapted from [5])
2. The Lieb-Oxford inquality (ref. [5])
3. The Lieb-Thirring inequality (ref. [2], [3], [4])
4. Kinetic energy inequalities (ref. [2], [3], [4])
5. The Araki-Lieb-Thirring operator trace inequality
(lecture notes,
adapted from Appendix 4.5 in [2], and
[Araki,1990])
6. Admissibility of the one particle density matrix
(
lecture notes, adapted from [2])
7. The Hardy-Littlewood maximal inequality
References
[1] E. H. Lieb. Thomas-fermi and related theories of atoms and molecules.
Rev. Mod. Phys. 1981.
[pdf]
[2] E. H. Lieb, R. Seiringer. Stability of matter in Quantum Mechanics.
Cambridge University Press.
[3] M. Loss. Stability of Matter. Lecture notes. [pdf]
[4] R. Seiringer. Inequalities for Schroedinger Operators and Applications to the Stability of Matter Problem. Lecture notes.
[pdf]
[5] E. H. Lieb, M. Loss. Analysis. American Mathematical Society.
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