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Computational Physics 2 (Simulation of Classical and Quantum Mechanical Systems)

Module PH2090

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.

Module version of SS 2019 (current)

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

available module versions
SS 2019SS 2018SS 2017SS 2011

Basic Information

PH2090 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • Specific catalogue of special courses for condensed matter physics
  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Complementary catalogue of special courses for Biophysics
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)

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

Total workloadContact hoursCredits (ECTS)
150 h 60 h 5 CP

Responsible coordinator of the module PH2090 is Stefan Recksiegel.

Content, Learning Outcome and Preconditions


Multiple subjects from Computational Physics are discussed:

  • Random Numbers
  • Fourier Transform
  • Nonlinear Systems and Chaos
  • Fractals
  • Time evolution of Quantum Wave Packets
  • Integral Equations
  • Finite Elements
  • Wavelets
  • Quantum Paths via Functional Integration
  • Introduction to Lattice Gauge Theory

Learning Outcome

After successful completion of this module, students are able to:

  • construct and solve numerical descriptions of classical and quantum mechanical problems.
  • apply ordinary and partial differential equations, Monte Carlo methods and chaos theory.
  • know (and rate) advanced numerical methods used in current research.


No preconditions in addition to the requirements for the Master’s program in Physics, but knowledge of the subjects covered in PH2057 is strongly recommended.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VU 4 Computational Physics 2: Simulation of Classical and Quantum Mechanical Systems Recksiegel, S. Tue, 14:00–16:00, PH HS3
and singular or moved dates
and dates in groups

Learning and Teaching Methods

This module consists of a lecture and an exercise class.

In the lecture, the contents are first explained on a theoretical level on an electronic whiteboard (the slides can be downloaded from the lecturer's web site immediately after the lectures). Then, the algorithms are implemented in the computer algebra system Mathematica to study the practical applicability of the concept. Whenever possible, the students are asked for input during this process, and if a suggested approach fails (e.g. due to numerical instabilities), the causes are discussed and alternatives are presented.

Exercise sheets (which frequently include reproduction of the results of the lecture) are first worked on individually by the students and then discussed in small groups under supervision.


Presentations on an electronic Whiteboard, demonstrations in Mathematica, C and Python ; exercise sheets. Accompanying web page:


  • R.H. Landau, M.J. Páez and C.C. Bordeianu: Computational Physics: Problem Solving with Computers, Wiley-Vch, (2007)
  • G.P. Lepage: Lattice QCD for Novices, arXiv, (2005),

Module Exam

Description of exams and course work

There will be a written exam of 90 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

  • Derive the formula for the discrete Fourier transform by evaluating the integral in the continuous Fourier transform with the trapezoidal rule. How many terms have to be calculated to transform N data points?
  • Give the DE that describes a pendulum with friction and a periodic driving force. How would you solve this DE numerically? Sketch several orbits in phase space.

Exam Repetition

The exam may be repeated at the end of the semester.

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