Mathematical Problems in Quantum Mechanics

by Serena Cenatiempo (GSSI)

Saturday 1 Feb 2020, 09:00 → Saturday 29 Feb 2020, 11:00 Europe/Rome

Lecturer
Serena Cenatiempo (GSSI)

Content
The class aim to provide an introduction to Quantum Mechanics, starting from the historical and experimental motivations which have lead to the introduction of the new theory. We will discuss the formalism of the theory and apply it to simple and paradigmatic one-particle models, such as the free particle, the harmonic oscillator and the hydrogen atom. 

The class will be a preparation to follow research seminars on some actual research lines in the mathematical analysis of quantum systems, which are scheduled during May/June 2020, including the following research seminars

• Interacting bosons in the Gross-Pitaevskii regime: statics and dynamics 
  (S.Cenatiempo, GSSI)
   
• Hydrodynamic Limit for a Disordered Quantum Harmonic Chain
  (A. Hannani, University Paris-Dauphine, PSL)

and the three short classes on Mathematical Methods in Field Theory and Quantum Mechanics, jointly organized by GSSI and SISSA.

Course requirements
Basic elements of the theory of linear operators in Hilbert spaces. 

References

• E.H.Lieb and R.Seiringer. The Stability of Matter in Quantum Mechanics. Cambridge, 2009.
• R. Seiringer. Cold Quantum Gases and Bose-Einstein Condensation. Lecture notes from the school ``Quantum Theory from Small to Large Scales'', August 2-27, 2010 [available here]
• A. Teta. A Mathematical Primer on Quantum Mechanics. Springer, 2018.

Examination and grading  
This class comes without any final exam, however written exercises will be suggested to the students during the course.