Doctoral position in Numerical Analysis

Academic staff

The goal of the project is the development of a posteriori error estimates for state-of-the-art numerical methods used to solve the electronic Schrödinger equation. The electronic Schrödinger equation is a high-dimensional eigenvalue problem that models the behavior of electrons in molecular systems using non-relativistic quantum mechanics. Cutting-edge numerical methods to solve this equation (such as coupled cluster or DMRG) involve the use of a low-rank, non-linear ansatz.

Analyzing such methods and developing a posteriori error estimates, therefore, requires tools from non-linear numerical analysis and high-dimensional approximation.

• must possess or be close to obtaining a master’s degree in applied mathematics with a focus on numerical analysis of PDEs.
• have an excellent knowledge of linear functional analysis.
• have experience with LaTeX and at least one scientific programming language, e.g., Julia, Python, or MATLAB.
• have solid spoken and written English communication skills.

Knowledge of German is not required. Prior knowledge of quantum physics is not required, but may be an advantage.

• The start date is negotiable, but ideally Spring 2026. The position is expected to last three years.
• The salary is based on the German public sector pay scale TV‑L E13 (75%). The actual salary depends on academic experience, family situation, tax classification, etc.
• Generous funding for travel to and participation in international conferences, workshops, and summer/winter schools is available.

This research position is funded by the DFG (German Research Foundation), so the PhD student’s primary responsibility will be to undertake research and disseminate their results through participation in scientific conferences and workshops and through publications. The PhD student will also be expected to participate in the supervision of BSc and MSc research projects, and will be encouraged to collaborate with colleagues working on electronic structure, both at TUM as well as at other universities.

There are no teaching obligations linked to the position, but opportunities are available within the department in case of interest.

Please send the following documents in a single file to .

• A CV.
• An academic transcript including a list of graduate courses taken and your grades.
• A copy of your MSc thesis. If you have not yet finished your thesis, then please include a copy of any significant mathematical work (e.g., a semester project report) of which you are the main author.
• Name and contact information of a referee.

In case of technical questions, please contact Muhammad Hassan via email: (Sie können sich bewerben oder uns per E-Mail kontaktieren in dem Sie die untenstehende Online-Bewerbungsbox verwenden) an equal‑opportunity and affirmative action employer, TUM explicitly encourages applications from women as well as from all others who would bring additional diversity dimensions to the university’s research and teaching strategies. Preference will be given to candidates with disabilities who have essentially the same qualifications.

Ziel des Projekts ist die Entwicklung von a-posteriori-Fehlerschätzungen für moderne numerische Methoden zur Lösung der elektronischen Schrödingergleichung. Die elektronische Schrödingergleichung ist ein hochdimensionales Eigenwertproblem, das das Verhalten von Elektronen in molekularen Systemen mithilfe der nichtrelativistischen Quantenmechanik modelliert. Moderne numerische Methoden zur Lösung dieser Gleichung (wie etwa Coupled Cluster oder DMRG) verwenden einen niedrig‑rangigen, nichtlinearen Ansatz. Die Analyse solcher Methoden und die Entwicklung von a-posteriori-Fehlerschätzungen erfordern daher Werkzeuge aus der nichtlinearen numerischen Analysis und der hochdimensionalen Approximation.

• verfügt über einen Masterabschluss in Angewandter Mathematik mit Schwerpunkt numerische Analysis von partiellen Differentialgleichungen oder steht kurz vor dem…