Time and place

Lecture: Mo, 12-14h, SR 404, Ernst-Zermelo-Str. 1

Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.

Teacher: Chiara Saffirio
Language: in English

This course provides an introduction to analytical methods in mathematical physics, with a particular emphasis on many-body quantum mechanics. A central focus is the rigorous proof of the stability of matter for Coulomb systems, such as atoms and molecules. The key question - why macroscopic objects made of charged particles do not collapse under electromagnetic forces - remained unresolved in classical physics and lacked even a heuristic explanation in early quantum theory. Remarkably, the proof of stability of matter marked the first time that mathematics offered a definitive answer to a fundamental physical and stands as one of the early triumphs of quantum mechanics.

Content:

• Mathematical background: \(L^p\) and Sobolev spaces; Fourier transform; \\
  
• Introduction to quantum mechanics and prototypical examples; \\
  
• Many-body quantum mechanics; \\
  
• Hamilton operator and its properties; Lieb-Thierring inequalities, electrostatic inequalities, Coulomb energy; \\
  
• Proof of Stability of Matter.

Analysis III and Linear Algebra are required. \
No prior knowledge of physics is assumed; all relevant physical concepts will be introduced from scratch.

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)