Entry requirements

1. Bachelor's degree of at least 180 credits within material engineering, machine engineering, physics, chemistry or the equivalent.

2. At least 22.5 credits of Mathematics.

3. English 6. Or: English level 2

Main field

CTMAV Materials Science

Progression level in relation to degree requirements

The course is included in the main field of materials science and may be included in a Master of Science (120 credits).

Course contents

• Wave–particle duality
• Time-dependent and time-independent Schrödinger equation
• The mathematical formalism and interpretation of quantum mechanics
• One-dimensional quantum systems
• One- and many-electron systems
• Chemical bonding
• Numerical methods for solving the Schrödinger equation

Learning outcomes

Knowledge and understanding

In order to pass the course, the student must be able to:

1. describe fundamental properties of quantum systems

2. explain central concepts such as wave–particle duality, wave function and superposition

3. formulate the Schrödinger equation for different systems

4. explain and give examples of how operators in quantum mechanics are used to represent observable physical quantities

5. explain central concepts such as probability, outcome, expectation value and uncertainty

6. explain the principles behind calculations of properties of many-electron systems

Skills and abilities

In order to pass the course, the student must be able to:

7. solve the Schrödinger equation exactly for simpler potentials and describe the main features of the solution and its properties for more advanced problems

8. calculate the probability of transmission through simpler potential structures and describe the qualitative properties of the wave function

9. derive fundamental operator relations and perform calculations with operators and perform approximate calculations of energies based on perturbation theory and variational methods

10. use numerical methods to solve quantum mechanical problems

Judgement and approach

In order to pass the course, the student must be able to:

11. assess the validity and limitations of different quantum mechanical models and reflect on how the choice of approximations affects the interpretation of physical results

Learning activities

Lectures, tutorials and computer laboratory work, self-study.

Assessment

Requirements for a Pass (UA)

• Computer laboratory assignments, 1.5 credits (Learning outcomes: 7–8, 10, 11, Pass/Fail)
• Written examination, 3.5 credits (Learning outcomes: 1–7, 9, 11, UA)

The final grade is based on the written examination.

Course literature and other study materials

• Jönsson, P. and Ekman, J. (2026) Lecture Notes in Quantum Mechanics, Department of Materials Science and Applied Mathematics, Malmö University

Course evaluation

Malmö University provides students who participate in, or who have completed a course, with the opportunity to express their opinions and describe their experiences of the course by completing a course evaluation administered by the University. The University will compile and summarise the results of course evaluations. The University will also inform participants of the results and any decisions relating to measures taken in response to the course evaluations. The results will be made available to the students (HF 1:14).

Interim rules

If a course is no longer offered, or has undergone significant changes, the students must be offered two opportunities for re-examination based on the syllabus that applied at the time of registration, for a period of one year after the changes have been implemented. The syllabus is a translation of a Swedish source text.

Additional information

If a student has a Learning support decision, the examiner has the right to provide the student with an adapted test, or to allow the student to take the exam in a different format. The syllabus is a translation of a Swedish source text.