Course syllabus

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TIF430 / FYM290 Quantum mechanics lp1 HT25 (4.5 hp)

The course is offered by the Department of Physics.

Contact details

Examiner:

  • Matthias Geilhufe, Assistant Professor, Condensed Matter and Materials Theory, Department of Physics, Chalmers

Teachers:

  • Finja Tietjen, PhD Student, Condensed Matter and Materials Theory, Department of Physics, Chalmers
  • Natalia Shabala, PhD Student, Condensed Matter and Materials Theory, Department of Physics, Chalmers

Student Representatives:

To be determined.

Course purpose

TIF290 / FYM290 is an advanced course on quantum mechanics. The purpose of the course is to:

  • Develop an abstract understanding of quantum mechanics and the capability to model quantum systems.
  • Interpret the implications of quantum mechanics and build an intuition for where quantum phenomena become relevant.
  • Develop the connection between the abstract mathematical formalism and applications, such as quantum technology and matter.

Schedule

TimeEdit

Course literature

Today, many fantastic books on quantum mechanics have been published, and most of the course content can be found in several books.

Traditionally, this course is based on:

  • J.J. Sakurai, Jim Napolitano, Modern Quantum Mechanics, Third Edition, Cambridge University Press, 2021.

Alternatives include:

  • Horațiu Năstase, Quantum Mechanics, Cambridge University Press, 2023.
  • Franz Schwabl, Quantum Mechanics, Fourth Edition, Springer, 2007.
  • John S. Townsend, A Modern Approach to Quantum Mechanics, California University Science Books, Second Edition, 2012.

Course design

The course consists of the following main components:

  • Lectures (16)
  • Homework assignments (3)
  • Exercise classes (3)
  • Research seminars (3)

Lectures

During the lectures, we will cover the main study material:

  • Foundations of quantum mechanics
  • Quantum dynamics
  • Matter in electromagnetic fields and light-matter interaction
  • Scattering theory

Homework Assignments

During the course, you will work on 3 homework assignments. By successfully solving a homework assignment, you can collect points. These points are relevant for the final exam. You need at least 6 points to participate in the final exam and at least 9 points to qualify for passing the exam with grades 4 or 5 (Chalmers) or VG (GU), respectively.

The due dates for the homework assignments will be:

  • Homework assignment 1: September 18, 2025, 23:59
  • Homework assignment 2: October 2, 2025, 23:59
  • Homework assignment 3: October 16, 2025, 23:59

Exercise classes

Throughout the exercise classes, we will discuss the most challenging tasks from the homework assignments, along with additional exercises to practice solving quantum mechanics problems. The exercise classes are given by the TAs.

Research Seminars

You will deepen your understanding of quantum mechanics through three research seminars. Here, you will explore lecture concepts by studying selected research articles. Participation in the research seminars is mandatory! The seminars are given by the TAs.

Changes made since the last occasion

New tasks have been added to the homework assignments. The exercise classes now include additional problem sets.

Learning objectives and syllabus

Foundations of quantum mechanics

  • Stern-Gerlach experiment
  • postulates of quantum mechanics
  • Dirac notation
  • noncommuting observables
  • Density operator; pure and mixed states; ensembles and open systems
  • quantum entanglement; Einstein-Podolsky-Rosen paradox; Bell's theorem and Bell tests

Quantum dynamics

  • time-evolution operator
  • Schrödinger and Heisenberg pictures
  • Rabi model
  • Jaynes-Cummings Hamiltonian
  • Correspondence principle; Ehrenfest's theorem
  • path integral formalism

Many-body physics

  • Second quantization
  • electrons / phonons / photons
  • interactions

Matter in electromagnetic fields and topology

  • Zeeman effect
  • Landau levels
  • gauge symmetry, geometric phase
  • Aharonov-Bohm effect

Scattering theory

  • Lippmann-Schwinger equation; Dyson equation; T-matrix
  • Born approximation
  • optical theorem

Additional Skills

  • Read scientific literature on the above topics

Links to the Syllabus on Studieportalen

Examination form

The final exam will be an oral exam. The final grade depends on your performance during the homework assignments. In the homework assignments, you need to collect a total of 6 points to qualify for the exam and potentially pass the course. You require at least 9 points to qualify for passing the exam with grades 4 or 5 (Chalmers) or VG (GU), respectively.  Furthermore, to qualify for the exam, you must have participated in the guest lecture(s) and mandatory research seminars. 

Every oral exam takes 30 minutes, with about 20 minutes of questions.

  • Date and time: week 44 (Oct 27 - Oct 31st). Individual time agreed on later throughout the course.

 

Course summary:

Date Details Due