MATH-561 / 5 credits

Teacher: Genoud François Samer

Language: English


Summary

This course is an introduction to the spectral theory of linear operators acting in Hilbert spaces. The main goal is the spectral decomposition of unbounded selfadjoint operators. We will also give elementary applications to quantum mechanics.

Content

Learning Prerequisites

Required courses

Analysis I-IV; Linear algebra; Functional analysis

Recommended courses

Measure and integration

Learning Outcomes

  • Prove properties of bounded and unbounded linear operators in Hilbert spaces
  • Solve problems involving symmetric / selfadjoint operators
  • Demonstrate a thorough understanding of the spectral decomposition theorem and of Stone's theorem
  • Explain how the theory provides the fundamental axioms of quantum mechanics

Assessment methods

Oral exam.

 

In case art. 3 al. 5 of the Règlement de section applies, the teacher communicates the form of the exam to the concerned students.

In the programs

  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Spectral theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Spectral theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Spectral theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Spectral theory
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
8-9   MAA330 
9-10    
10-11   MAA330 
11-12    
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     

Thursday, 8h - 10h: Lecture MAA330

Thursday, 10h - 12h: Exercise, TP MAA330