A striking success of quantum mechanics is the fact that, in contrast to the classical theory, it explains the stability of matter, as we observe it in everyday life. The rigorous verification of this property starting from the basic assumptions of quantum mechanics required deep analytic tools and represented a major achievement in mathematical physics. The goal of this class is to present a proof of stability of matter and to discuss some related mathematical questions. We will start by reviewing the main postulates of quantum mechanics, focusing in particular on many-body theory. We will then explain the problem of stability and we will introduce some important tools that are needed for its proof. Afterwards, we will present some important approximation of the quantum theory of atoms and molecules, focusing in particular on Thomas-Fermi theory and, if time permits, on Hartree- Fock theory.
Notes for videos:
Due to the COVID-19 pandemic, from Oct. 26 classes do not take place on campus. Students registered to the class will receive instead links to videos of recorded lectures. The notes of the video lectures are available here:
Video Lecture 26.10 - Virial identities, no-binding
Zoom Lecture 28.10 - Connections between TF theory and many body QM
Zoom Lecture 02.11 - Towards an upper bound for quantum energy
Zoom Lecture 04.11 - Upper bound for quantum energy
Zoom Lecture 09.11 - Lower bound for quantum energy
Zoom Lecture 11.11 - Introduction to Hartree-Fock theory
Zoom Lecture 16.11 - Correlation inequalities I
Zoom Lecture 18.11 - Correlation inequalities II
Zoom Lecture 23.11 - Semiclassical approximation
Zoom Lecture 25.11 - From quantum mechanics to Hartree-Fock I
Zoom Lecture 30.11 - From quantum mechanics to Hartree-Fock II
Zoom Lecture 02.12 - Chandrasekhar theory of stellar collapse
Zoom Lecture 07.12 - Chandrasekhar energy as upper bound for quantum energy
Zoom Lecture 09.12 - Chandrasekhar energy as lower bound for quantum energy
Zoom Lecture 09.12 - From quantum to Chandrasekhar: conclusion of the proof
E. H. Lieb, R. Seiringer. The stability of matter in quantum mechanics. Cambridge University Press, 2010.
E.H. Lieb. Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys. 53, 603-641 (1981).
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