Computational Quantum Mechanics (honours)

Course manual 2025/2026

Course content

This course provides an introduction to computational methods used to numerically solve quantum mechanical problems, building upon concepts introduced in Quantum Physics 1 and 2. Students will learn to apply state-of-the-art numerical techniques to solve the time-independent and time-dependent Schrödinger equation and apply these methods to various physical systems. The goal is to give students both a deep understanding of quantum phenomena and practical skills in computational physics.

As part of this lecture course, students will select a research paper that outlines the implementation and application of a numerical technique. They will be expected to thoroughly read and understand the paper, implement and test the described method, and present their findings in a concise presentation. The developed code, along with a brief written report, will also be submitted as part of the project.

At the end of the class each student has a code library to calculate energies and wavefunction of a particle in a box, the particle on a ring, the harmonic and anharmonic oscillator, the hydrogen and helium atom, the hydrogen molecular ion; as well as to propagate a wave packet in time and space.

Numerical techniques covered include: the Numerov method, Discrete-Variable Representation, Split-Operator Method, Crank–Nicolson method, Richardson extrapolation and more.

You will learn (to):

• Derive and implement tailored solvers instead of relying on black-box ODE libraries.

• Time-independent methods: Numerov; Discrete-Variable Representation (DVR).

• Time-dependent methods: Crank–Nicolson; split-operator.

• Starting integrations and handling singularities via series solutions.

• Check numerical stability with von Neumann (Fourier) stability analysis.

• Improve accuracy using Richardson extrapolation.

• Build Wronskians & Green’s functions numerically and use them in practice.

• Implement numerical versions of perturbation theory and the variational principle.

• Include many-body physics: Hartree treatment of electron–electron repulsion.

• Compute scattering observables, e.g., atom–atom cross sections and photoionization cross sections.

What you’ll build:

By the end of the course, you’ll have a personal code library to:

• compute energies and wavefunctions for 1D/2D boxes, rings, harmonic and anharmonic oscillators, H and He atoms, H2+

• propagate wave packets in time and space,

• benchmark, document, and package your implementations for reuse.

How the course works:

• Foundations in seminar style. Short lectures establish the physics and numerics.

• Paper-to-practice project. Pick a research paper, implement the method, test it, and present your results.

• Deliverables. Final presentation + short report; your code is bundled into a shared course library.

Study materials

Literature

• Parts of D.J. Griffiths, `Introduction to Quantum Mechanics'. 

• Articles, book chapters, and written lecture notes (Canvas).

Syllabus

• Canvas

Software

• Python/Matlab/Julia/Mathematica/Fortran (free choice)

Objectives

• Demonstrate understanding of numerical techniques to solve the Schrödinger equation, applying perturbation and variational techniques.
• Learning to read research papers, implement and test numerical techniques using various programming languages.

Teaching methods

• Laptop seminar
• Self-study
• Seminar
• Presentation/symposium

Learning activities

Attendance

Programme's requirements concerning attendance (TER-B):

• Each student is expected to participate actively in each component of the programme that he/she signed up for. A student that does not attend the first two seminars of a course, will be administratively removed from the seminar group. A request for reregistration for the seminars can be applied to the programme coordinator.
• If a student cannot attend an obligatory component of a programme's component due to circumstances beyond his control, he must report in writing to the relevant teacher as soon as possible. The teacher, if necessary after consulting the study adviser, may decide to issue the student a replacing assignment.
• It is not allowed to miss obligatory commponents of the programme if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are set down in advance in the course manual.

Assessment

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Contact information

Coordinator

• dr. M. Beyer