Information Package / Course Catalogue
Special Functions in Physics
Course Code: FİZ328
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 4
Objectives of the Course

Learning special functions and investigating the physical applications of them.

Course Content

Gamma and Beta functions, Legendre polynomials, Bessel functions, Laguerre functions, Hermite polynomials.

Name of Lecturer(s)
Learning Outcomes
1.Must be able to define gamma and beta functions.
2.Must be able to define the Dirac Delta function and use it in physical problems.
3.Must be able to use separation of variables to solve some important PDEs in physics.
4.Must be able to apply the power series method to ODE.
5.Must be able to solve Legendre differential equation to obtain Legendre polynomials, and to use the properties of Legendre polynomials.
6.Must be able to solve Bessel differential equation to obtain Bessel functions, and to use the properties of Bessel functions.
7.Must be able to state that the solutions of the radial Schrodinger equation in three dimensions for a free particle are expressed by Bessel functions.
8.Must be able to say that the wave functions of the harmonic oscillator can be expressed by Hermite polynomials.
9.Must be able to express that for spherically symmetric potentials, the angular part of the wave function gives spherical harmonic functions.
10.Must be able to express the relationship between the angular momentum operator and spherical harmonic functions in quantum mechanics.
11.Must be able to express the relationship between the hydrogen atom and Laguerre polynomials.
Recommended or Required Reading
1.Mathematical Methods in The Physical Sciences, Mary L. Boas
2.Mathematical Methods for Physicists, George B. Arfken
3.Special Functions and Their Applications, N. N. Lebedev
4.Special Functions, Nico M. Temme
Weekly Detailed Course Contents
Week 1 - Theoretical
Gama, beta and error functions
Week 2 - Theoretical
Asymptotic Series
Week 3 - Theoretical
Stirring formula.
Week 4 - Theoretical
Elliptic integrals and functions.
Week 5 - Theoretical
Dirac Delta functions
Week 6 - Theoretical
Partial differential equations (PDE) in physics and separation of variables.
Week 7 - Theoretical
Solutions of differential equations by power series methods.
Week 8 - Theoretical
Review (Midterm Exam)
Week 9 - Theoretical
Legendre functions
Week 10 - Theoretical
Associated Legendre functions.
Week 11 - Theoretical
Bessel functions.
Week 12 - Theoretical
Spherical harmonics
Week 13 - Theoretical
Laguerre functions.
Week 14 - Theoretical
Hermite functions
Assessment Methods and Criteria
Type of AssessmentCountPercent
Attending Lectures1%5
Quiz2%5
Midterm Examination1%30
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140342
Quiz24010
Midterm Examination122224
Final Examination122224
TOTAL WORKLOAD (hours)100
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
OÇ-1
2
4
5
1
OÇ-2
2
3
4
OÇ-3
3
3
4
OÇ-4
2
2
4
OÇ-5
3
4
5
OÇ-6
3
4
5
OÇ-7
3
4
4
OÇ-8
3
4
5
3
OÇ-9
3
4
4
OÇ-10
3
4
4
OÇ-11
3
4
4
Adnan Menderes University - Information Package / Course Catalogue
2026