Special Functions in Theoretical Physics

Module PH8101

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

PH8101 is a semester module in German or English language at Bachelor’s level which is offered irregular.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
90 h 30 h 3 CP

Responsible coordinator of the module PH8101 is Norbert Kaiser.

Content, Learning Outcome and Preconditions


Complex-valued functions of a complex variable, complex differentiation, complex line integrals and Cauchy theorem, residue theorem, applications of residue calculus, Legendre polynomials and their properties, sperical harmonics and their properties, Bessel functions, spherical Bessel functions, orthogonal polynomials, solving the wave equation in 1,2 and  3,space dimentions.

Learning Outcome

The student knows the restrictive properties of complex differentiable functions,

The student how know to use residue calculus for evaluating definite integrals.

The student knows the proerties of Legendre polynomials, sperical harmionics, Bessel functions and spherical Bessel functions.

The student knows the most important sets of orthogonal polynomials relevant for quantum mechanics.

The student knows the different behavior of solutions of the wave equation depending on the space dimension.



Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

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Module Exam

Description of exams and course work

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Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.