Mathematical aspects of quantum physics
Summary
This lecture is a more advanced course in fonctionnel Analysis, presenting techniques with spécial interests for quantum Mechanics
Content
Nuclear spaces
Schwartz Nuclear théorèm.
Nuclear spectral théorèm.
Functionnal intégration
Brownian motions
Bochner-Minlos théorèm.
Keywords
distributions.
family of semi-norms
functionnal integration
Learning Prerequisites
Required courses
Analysis 1 to 4
Advanced linear algebra
mathematical methods for physicists
Quantum mechanic I and II
Important concepts to start the course
Basic topology
Hilbert and Banach spaces
Lebesgue integration
Learning Outcomes
By the end of the course, the student must be able to:
- Transcribe physics in math
- Develop
- Model
Transversal skills
- Continue to work through difficulties or initial failure to find optimal solutions.
- Demonstrate the capacity for critical thinking
- Demonstrate a capacity for creativity.
- Communicate effectively, being understood, including across different languages and cultures.
Teaching methods
Ex-cathedra
Expected student activities
The students are expected to participate actively in the lecture.
Assessment methods
The exam will be in oral form.
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
Kaballo: "aufbaukurs in Funktionalanalysis"
Wightmann "spin, statistics and all that"
Hida "brownian motion"
Ressources en bibliothèque
- Aufbaukurs Funktionalanalysis und Operatortheorie / Kaballo
- PCT, spin and statistics, and all that / Streater
- Brownian motion / Hida
Notes/Handbook
not yet but under construction
Websites
Videos
Prerequisite for
Research in mathematical or theoretical physics
In the programs
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Mathematical aspects of quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Mathematical aspects of quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Mathematical aspects of quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Oral (winter session)
- Subject examined: Mathematical aspects of quantum physics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional