Masters degrees in Quantum Mechanics involve advanced study of material properties and processes at the sub-atomic level.
Related subjects include Quantum Technologies and Microsystems Engineering. Entry requirements typically include an undergraduate degree in an appropriate field such as Physics, Chemistry or an Engineering subject.
Courses in this field examine the experimental and theoretical developments associated with understanding the energy levels of atoms and subatomic particles. The study of Quantum Mechanics can develop highly precise materials, technology, and processes, improving the objects that we use in our daily lives.
Quantum Mechanics may be applied to a range of industries, most popularly those in technology and engineering. For example, you might explore superconductors and simulators to assess how materials respond to different forces of energy. This expertise in turn may be applied to automotive and aerospace engineering, and the product development of items such as safety apparel.
Alternatively, you might focus on quantum information technology, developing photonics and optical communications, as well as computer programming and software development.
Finally, you could specialise in high-precision measurements and quantum metrology, which can be applied to security systems and the development of laser technology, satellite communications and radar.
Working at a frontier of mathematics that intersects with cutting edge research in physics.
Mathematicians can benefit from discoveries in physics and conversely mathematics is essential to further excel in the field of physics. History shows us as much. Mathematical physics began with Christiaan Huygens, who is honoured at Radboud University by naming the main building of the Faculty of Science after him. By combining Euclidean geometry and preliminary versions of calculus, he brought major advances to these areas of mathematics as well as to mechanics and optics. The second and greatest mathematical physicist in history, Isaac Newton, invented both the calculus and what we now call Newtonian mechanics and, from his law of gravity, was the first to understand planetary motion on a mathematical basis.
Of course, in the Master’s specialisation in Mathematical Physics we look at modern mathematical physics. The specialisation combines expertise in areas like functional analysis, geometry, and representation theory with research in, for example, quantum physics and integrable systems. You’ll learn how the field is far more than creating mathematics in the service of physicists. It’s also about being inspired by physical phenomena and delving into pure mathematics.
At Radboud University, we have such faith in a multidisciplinary approach between these fields that we created a joint research institute: Institute for Mathematics, Astrophysics and Particle Physics (IMAPP). This unique collaboration has lead to exciting new insights into, for example, quantum gravity and noncommutative geometry. Students thinking of enrolling in this specialisation should be excellent mathematicians as well as have a true passion for physics.
See the website http://www.ru.nl/masters/mathematics/physics
- This specialisation is one of the few Master’s in the world that lies in the heart of where mathematics and physics intersect and that examines their cross-fertilization.
- You’ll benefit from the closely related Mathematics Master’s specialisations at Radboud University in Algebra and Topology (and, if you like, also from the one in Applied Stochastics).
- Teaching takes place in a stimulating, collegial setting with small groups. This ensures that at Radboud University you’ll get plenty of one-on-one time with your thesis supervisor.
- You partake in the Mastermath programme, meaning you can follow the best mathematics courses, regardless of the university in the Netherlands that offers them. It also allows you to interact with fellow mathematic students all over the country.
- As a Master’s student you’ll get the opportunity to work closely with the mathematicians and physicists of the entire IMAPP research institute.
- More than 85% of our graduates find a job or a gain a PhD position within a few months of graduating. About half of our PhD’s continue their academic careers.
Mathematicians are needed in all industries, including the industrial, banking, technology and service industry and also within management, consultancy and education. A Master’s in Mathematics will show prospective employers that you have perseverance, patience and an eye for detail as well as a high level of analytical and problem-solving skills.
The skills learned during your Master’s will help you find jobs even in areas where your specialised mathematical knowledge may initially not seem very relevant. This makes your job opportunities very broad indeed and is why many graduates of a Master’s in Mathematics find work very quickly.
Possible careers for mathematicians include:
- Researcher (at research centres or within corporations)
- Teacher (at all levels from middle school to university)
- Risk model validator
- ICT developer / software developer
- Policy maker
Radboud University annually has a few PhD positions for graduates of a Master’s in Mathematics. A substantial part of our students attain PhD positions, not just at Radboud University, but at universities all over the world.
The research of members of the Mathematical Physics Department, emphasise operator algebras and noncommutative geometry, Lie theory and representation theory, integrable systems, and quantum field theory. Below, a small sample of the research our members pursue.
Gert Heckman's research concerns algebraic geometry, group theory and symplectic geometry. His work in algebraic geometry and group theory concerns the study of particular ball quotients for complex hyperbolic reflection groups. Basic questions are an interpretation of these ball quotients as images of period maps on certain algebraic geometric moduli spaces. Partial steps have been taken towards a conjecture of Daniel Allcock, linking these ball quotients to certain finite almost simple groups, some even sporadic like the bimonster group.
Erik Koelink's research is focused on the theory of quantum groups, especially at the level of operator algebras, its representation theory and its connections with special functions and integrable systems. Many aspects of the representation theory of quantum groups are motivated by related questions and problems of a group representation theoretical nature.
Klaas Landsman's previous research programme in noncommutative geometry, groupoids, quantisation theory, and the foundations of quantum mechanics (supported from 2002-2008 by a Pioneer grant from NWO), led to two major new research lines:
1. The use of topos theory in clarifying the logical structure of quantum theory, with potential applications to quantum computation as well as to foundational questions.
2. Emergence with applications to the Higgs mechanism and to Schroedinger's Cat (aka as the measurement problem). A first paper in this direction with third year Honours student Robin Reuvers (2013) generated worldwide attention and led to a new collaboration with experimental physicists Andrew Briggs and Andrew Steane at Oxford and philosopher Hans Halvorson at Princeton.
See the website http://www.ru.nl/masters/mathematics/physics
Revealing the ‘terra incognita’ between quantum mechanics and the classical world and inspiring new technologies.
As a scientist, you’re a problem solver. But how do you tackle a problem when there are no adequate theories and calculations become far too complicated? In the specialisation in Physics of Molecules and Materials you’ll be trained to take up this challenge in a field of physics that is still largely undiscovered: the interface between quantum and classical physics.
We focus on systems from two atoms to complete nanostructures, with time scales in the order of femtoseconds, picoseconds or nanoseconds. One of our challenges is to understand the origin of phenomena like superconductivity and magnetism. As theory and experiment reinforce each other, you’ll learn about both ‘research languages’. In this way, you’ll be able to understand complex problems by dividing them into manageable parts.
See the website http://www.ru.nl/masters/physicsandastronomy/physics
- At Radboud University there’s a strong connection between theory and experiment. Theoretical and experimental physicists will teach you to become acquainted with both methods.
- In your internship(s), you’ll have the opportunity to work with unique research equipment, like free electron lasers and high magnetic fields, and with internationally known scientists.
- We collaborate with several industrial partners, such as Philips and NXP. This extensive network can help you find an internship or job that meets your interests.
If you’re successful in your internship, you have a good chance of obtaining a PhD position at the Institute for Molecules and Materials (IMM).
1. A completed Bachelor's degree in Physics
2. A proficiency in English
In order to take part in this programme, you need to have fluency in both written and spoken English. Non-native speakers of English* without a Dutch Bachelor's degree or VWO diploma need one of the following:
- A TOEFL score of ≥575 (paper based) or ≥90 (internet based
- An IELTS score of ≥6.5
- Cambridge Certificate of Advanced English (CAE) or Certificate of Proficiency in English (CPE) with a mark of C or higher.
This Master’s specialisation is an excellent preparation for a career in research, either at a university or at a company. However, many of our students end up in business as well. Whatever job you aspire, you can certainly make use of the fact that you have learned to:
- Solve complex problems
- Make accurate approximations
- Combine theory and experiments
- Work with numerical methods
Graduates have found jobs as for example:
- Consultant Billing at KPN
- Communications advisor at the Foundation for Fundamental Research on Matter (FOM)
- Systems analysis engineer at Thales
- Technical consultant at UL Transaction Security
- Business analyst at Capgemini
At Radboud University, we’re capable of offering many successful students in the field of Physics of Molecules and Materials a PhD position. Many of our students have already attained a PhD position, not just at Radboud University, but at universities all over the world.
In this specialisation, you’ll discover the interface between quantum mechanics and the classical world, which is still a ‘terra incognita’. We focus on two-atom systems, multi-atom systems, molecules and nanostructures. This is pioneering work, because these systems are often too complex for quantum calculations and too small for the application of classical theories.
- Theory and experiment
At Radboud University, we believe that the combination of theory and experiments is the best way to push the frontiers of our knowledge. Experiments provide new knowledge and data and sometimes also suggest a model for theoretical studies. The theoretical work leads to new theories, and creative ideas for further experiments. That’s why our leading theoretical physicists collaborate intensively with experimental material physicists at the Institute for Molecules and Materials (IMM). Together, they form the teaching staff of the Master’s specialisation in Physics of Molecules and Materials.
This specialisation is focused on two main topics:
- Advanced spectroscopy
Spectroscopy is a technique to look at matter in many different ways. Here you’ll learn the physics behind several spectroscopic techniques, and learn how to design spectroscopic experiments. At Radboud University, you also have access to large experimental infrastructure, such as the High Magnetic field Laboratory (HFML), the FELIX facility for free electron lasers and the NMR laboratory.
- Condensed matter and molecular physics
You’ll dive into material science at the molecular level as well as the macroscopic level, on length scales from a single atom up to nanostructure and crystal. In several courses, you’ll get a solid background in both quantum mechanical and classical theories.
We’re not aiming at mere evolution of current techniques, we want to revolutionize them by developing fundamentally new concepts. Take data storage. The current data elements are near the limits of speed and data capacity. That’s why in the IMM we’re exploring a completely new way to store and process data, using light instead of electrical current. And this is but one example of how our research inspires future technology. As a Master’s student you can participate in this research or make breakthroughs in a field your interested in.
See the website http://www.ru.nl/masters/physicsandastronomy/physics
This is a one year advanced taught course. The aim of this course is to bring students in 12 months to the frontier of elementary particle theory. This course is intended for students who have already obtained a good first degree in either physics or mathematics, including in the latter case courses in quantum mechanics and relativity.
The course consists of three modules: the first two are the Michaelmas and Epiphany graduate lecture courses, which are assessed by examinations in January and March. The third module is a dissertation on a topic of current research, prepared under the guidance of a supervisor with expertise in the area. We offer a wide variety of possible dissertation topics. The dissertation must be submitted by September 15th, the end of the twelve month course period.
The main group of lectures are given in the first two terms of the academic year (Michaelmas and Epiphany). This part of the lecture course is assessed by examinations. In each term there are two teaching periods of four weeks, with a week's break in the middle of the term in which students will be able to revise the material. Most courses are either eight lectures or 16 lectures in length. There are 14 lectures/week in the Michaelmas term and 14 lectures/week in Epiphany term.
Optional Modules available in previous years included:
This is a full-year degree course, starting early October and finishing in the middle of the subsequent September. The aim of the course is to bring students to the frontier of research in elementary particle theory.
The course consists of three modules: the first two are the Michaelmas and Epiphany graduate lecture courses. The third module is a dissertation on a topic of current research, prepared under the guidance of a supervisor with expertise in the area. We offer a wide variety of possible dissertation topics.
The lectures begin with a general survey of particle physics and introductory courses on quantum field theory and group theory. These lead on to more specialised topics, amongst others in string theory, cosmology, supersymmetry and more detailed aspects of the standard model.
The main group of lectures is given in the first two terms of the academic year (Michaelmas and Epiphany). This part of the lecture course is assessed by examinations. In each term there are two teaching periods of 4 weeks, with a week's break in the middle of the term in which students will be able to revise the material. Most courses are either 8 lectures or 16 lectures in length. There are 14 lectures/week in the Michaelmas term and 14 lectures/week in Epiphany term they are supported by weekly tutorials. In addition lecturers also set a number of homework assignments which give the student a chance to test his or her understanding of the material.
There are additional optional lectures in the third term. These introduce advanced topics and are intended as preparation for research in these areas.
The dissertation must be submitted by mid-September, the end of the twelve month course period.
This course aims to bring you, in 12 months, to a position where you can embark with confidence on a wide range of careers, including taking a PhD in Mathematics or related disciplines. There is a wide range of taught modules on offer, and you will also produce a dissertation on a topic of current research interest taken from your choice of a wide range of subjects offered.
Modules: Six of available options
In previous years, optional modules available included:
Modules in Pure Mathematics:
Modules in Probability and Statistics:
Modules in Applications of Mathematics:
This is a full-year degree course, starting early October and finishing in the middle of the subsequent September. The aim of the course is to give the students a wide mathematical background allowing them to either proceed to PhD or to apply the gained knowledge in industry.
The course consists of three modules: the first two are the Michaelmas and Epiphany lecture courses covering variety of topics in pure and applied mathematics and statistics. The third module is a dissertation on a topic of current research, prepared under the guidance of a supervisor with expertise in the area. We offer a wide variety of possible dissertation topics.
The main group of lectures is given in the first two terms of the academic year (Michaelmas and Epiphany), there are also two revision lectures in the third term (Easter). This part of the course is assessed by examinations. Students choose 6 modules, each module has 2 lectures per week and one fortnightly problems class. There are 10 teaching weeks in the Michaelmas term and 9 teaching weeks in Epiphany term. In addition lecturers also set a number of homework assignments which give the student a chance to test their understanding of the material.
The dissertation must be submitted by mid-September, the end of the twelve month course period
This programme reflects and benefits from the strong research activities of the Department of Mathematics.
The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups:
During the first two semesters you will take a range of taught modules from an extensive list of options, followed by an extended research project conducted over the summer under the supervision of a member of the department, culminating in the writing of a dissertation.
This programme is studied full-time over one academic year. It consists of eight taught modules and a dissertation.
Example module listing
The following modules are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.
Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management.
There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.
As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied.
Knowledge and understanding
Intellectual / cognitive skills
Professional practical skills
Key / transferable skills
We often give our students the opportunity to acquire international experience during their degrees by taking advantage of our exchange agreements with overseas universities.
In addition to the hugely enjoyable and satisfying experience, time spent abroad adds a distinctive element to your CV.
Degree: Master of Science (two years) with a major in Applied Physics or Master of Science (two years) with a major in Physics
Teaching language: English
The Material Physics and Nanotechnology master's programme provides students with specialist knowledge in the area of new materials. Huge advances in modern technology and products in recent decades have to a large extent relied on developments in this field.
The importance of advanced materials in today’s technology is best exemplified by the highly purified semiconductor crystals that are the basis of the electronic age. Future implementations and applications of materials in electronics and photonics involve such subjects as nano-scale physics, molecular electronics and non-linear optics.
With support from internationally competitive research activities in materials physics at Linköping University, the programme has been established with distinct features that offer students high‑level interdisciplinary education and training in fundamental solid state physics and materials science within the following areas:
The programme emphasises the comprehension of scientific principles and the development of personal and professional skills in solving practical engineering problems. Studies begin with mandatory courses, including nanotechnology, quantum mechanics, surface physics and the physics of condensed matter, in order to provide students with a solid knowledge foundation for modern materials science and nanotechnology. Moreover, through courses in experimental physics and analytical methods in materials science, students gain extensive training in operating the advanced instruments and equipment currently used in the research and development of new materials.
A variety of elective courses is offered from the second term onwards, many of them involving the use of cutting-edge technology. These courses give students a broad perspective of today’s materials science research and links to applications in semiconductor technology, optoelectronics, bioengineering (biocompatibility), chemical sensors and biosensors, and mechanical applications for high hardness and elasticity. Students will also be instructed through in-depth CDIO (Conceive – Design – Implement – Operate) project courses, to develop abilities in creative thinking and problem solving.
Students complete a thesis project in the area of materials science and nanotechnology, either with an in-house research group or the industry.
With the MSc Physics you will develop a rounded education across the breadth of physics with an in-depth research project, supported by expert academics. You will learn to communicate to a broad audience and make physics accessible for all on current topics in physics. You will present your understanding through innovative techniques including vlogging, infographics, patents, apps, outreach experiments and articles for The Conversation.
Develop your practical skills and theoretical knowledge in a specialist area of physics with the MRes Physics, according to your personal aspirations. You will combine taught modules with a year-long extended project whereby the course* will help you gain extensive knowledge in a particular subject area, as you develop vital research skills.
You will be taught by experienced academics discussing forefront industry topics such as nanotechnology, space weather and upper atmosphere and applications for micro-fluidic fundamentals.
Visit us on campus throughout the year, find and register for our next open event on http://www.ntu.ac.uk/pgevents.