Information Package / Course Catalogue
Functional Analysis For Physicists
Course Code: FZK527
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: Turkish
Work Placement: 
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

Description of functional analysis which is the mathematical basis of quantum mechanics

Course Content

Linear spaces, linear operators, operator algebra, apllication to quantum mechanics

Name of Lecturer(s)
Learning Outcomes
1.To be able to express the definition of linear vector spaces
2.To be able to perform the spectral decomposition of self-adjoint operators
3.To be able to explain the operator core concept
4.To be able to explain the difference between the concepts of state and observable
5.To be able to apply the functional analysis methods to quantum mechanical problems
Recommended or Required Reading
1.Linear Operators for Quantum mechanics, T. F. Jordan, 1997, Dover, New York
2.Theory of Linear Operators in Hilbert Space, N.I. Akhiezer, I.M.Glazman, 1993, Dover, NewYork
3.Introductory Functional Analysis with Applications, Erwin Kreyzig
4.Calculus, T.M. Apostol, 2.ed, 1967, New York, John Wiley Sons
Weekly Detailed Course Contents
Week 1 - Theoretical
Metric spaces
Week 1 - Preparation Work
Apostol T.M., Calculus, Chapter2
Week 2 - Theoretical
Normed spaces, Banach spaces
Week 2 - Preparation Work
Kreyzig E, Introductory Functional Analysis with Applications, Chapter2
Week 3 - Theoretical
Inner product spaces and Hilbert spaces
Week 3 - Preparation Work
Thomas F., Linear Operators for Quantum mechanics, Section 1.3
Week 4 - Theoretical
Linear functionals
Week 4 - Preparation Work
Thomas F., Linear Operators for Quantum mechanics, Section 1.4
Week 5 - Theoretical
Bounded linear operators
Week 5 - Preparation Work
Thomas F., Linear Operators for Quantum mechanics, Section 2.1-2,3
Week 6 - Theoretical
Projection operators
Week 6 - Preparation Work
Thomas F., Linear Operators for Quantum mechanics, Section 2.10
Week 7 - Theoretical
Unitary operators
Week 7 - Preparation Work
Akhiezer L.I, Glazman I.M., Theory of Linear Operators in Hilbert Space, Section 3.35
Week 8 - Theoretical
Closed operators and adjoint of an operator(Midterm Exam)
Week 8 - Preparation Work
Akhiezer L.I, Glazman I.M., Theory of Linear Operators in Hilbert Space, Section 4.38
Week 9 - Theoretical
Self-adjoint operators
Week 9 - Preparation Work
Akhiezer L.I, Glazman I.M., Theory of Linear Operators in Hilbert Space, Section 4.39
Week 10 - Theoretical
Concept of spectrum
Week 10 - Preparation Work
Akhiezer L.I, Glazman I.M., Theory of Linear Operators in Hilbert Space, Section 4.41; Thomas F., Linear Operators for Quantum mechanics, Section 3.12, 3.13
Week 11 - Theoretical
Core of an operator
Week 11 - Preparation Work
Akhiezer L.I, Glazman I.M., Theory of Linear Operators in Hilbert Space, Section 4.44
Week 12 - Theoretical
Spectral analysis of unitary and self-adjoint operators
Week 12 - Preparation Work
Thomas F., Linear Operators for Quantum mechanics, Section 2.14
Week 13 - Theoretical
Spectral analysis of unitary and self-adjoint operators
Week 13 - Preparation Work
Thomas F., Linear Operators for Quantum mechanics, Section 2.15
Week 14 - Theoretical
Self-adjoint extension of operators
Week 14 - Preparation Work
Akhiezer L.I, Glazman I.M., Theory of Linear Operators in Hilbert Space, Chapter5
Assessment Methods and Criteria
Type of AssessmentCountPercent
Attending Lectures1%5
Assignment1%5
Midterm Examination1%30
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Assignment1246
Midterm Examination126430
Final Examination126430
TOTAL WORKLOAD (hours)150
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
OÇ-1
5
2
3
3
1
3
1
2
OÇ-2
5
2
3
3
1
3
1
1
OÇ-3
5
4
4
3
2
3
1
3
OÇ-4
5
4
4
3
1
4
1
1
OÇ-5
5
2
4
3
1
3
1
1
Adnan Menderes University - Information Package / Course Catalogue
2026