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Quantum Mechanics 2


Admission requirements

Quantum Mechanics 1, Statistical Physics 1, Classical Mechanics B, AN3na, LA2na


This course deepens the understanding of quantum mechanics by studying important quantum phenomena and applications of quantum mechanics in technologies like MRI and the laser.

The following topics are treated:

  • Quantum statistical description of indistinguishable particles

  • Fermi-Dirac, Bose-Einstein, and Planck distributions

  • The free electron gas, Bose-Einstein condensation, and the law of Stefan and Boltzmann.

  • The structure of atoms and the Periodic Table

  • Time-independent perturbation theory and application in the fine-structure and hyperfinestructure in the spectrum of the hydrogen atom

  • Influence of external magnetic field (Zeeman-effect) and electrical field (Stark-effect) on spectral lines

  • Time-dependent perturbation theory and application to two-level systems

  • Nuclear magnetic resonance and its use in Magnetic Resonance Imaging (MRI).

  • Einstein theory of radiation processes: absorption, stimulated and spontaneous emission and its use in the laser.

  • selection rules for radiative transitions
    An introduction to more advanced and/or modern topics in quantum mechanics is given: Dirac equation for relativistic electrons, entanglement, and quantum computers.

Course objectives

After the course the student will be able to discuss and explain the following concepts and topics and to apply these concepts in calculations:

  • Quantum statistical description of indistinguishable particles

  • Fermi-Dirac, Bose-Einstein and Planck distribution

  • Properties of the free electron gas, the free Bose gas, and the role of the density of states

  • How quantum mechanics averts the ultraviolet catastrophy

  • Apply time-independent perturbation theory to calculate the fine-structure and hyperfinestructure of the spectrum of hydrogen atoms

  • How external magnetic (Zeeman-effect) and electrical fields (Stark-effect) affect the spectra of atoms

  • Apply time-dependent perturbation theory to two-level systems and explain the essence of magnetic resonance imaging

  • Explain the radiative processes: absorption, stimulated and spontaneous emission (Einstein theory) and perform calculations of the corresponding transition rates.

You will be able to explain or describe in your own words the following concepts or topics:

  • How the laser (and maser) work

  • Entanglement and quantum information

  • Dirac equation for relativistic electrons

Transferable Skills

  • You are able to paraphrase your reasonings clearly

  • You plan your time in such a way that your study load is well divided over the various study activities that are needed in this course: studying the book, preparing for lectures and tutorials(exercise classes), working out exercises, and preparing for the exam.


For detailed information go to Timetable in Brightspace

You will find the timetables for all courses and degree programmes of Leiden University in the tool MyTimetable (login). Any teaching activities that you have sucessfully registered for in MyStudyMap will automatically be displayed in MyTimeTable. Any timetables that you add manually, will be saved and automatically displayed the next time you sign in.

MyTimetable allows you to integrate your timetable with your calendar apps such as Outlook, Google Calendar, Apple Calendar and other calendar apps on your smartphone. Any timetable changes will be automatically synced with your calendar. If you wish, you can also receive an email notification of the change. You can turn notifications on in ‘Settings’ (after login).

For more information, watch the video or go the the 'help-page' in MyTimetable. Please note: Joint Degree students Leiden/Delft have to merge their two different timetables into one. This video explains how to do this.

Mode of instruction

See Brightspace
Lectures, tutorials (exercise classes) and homework assignments. The lectures are in Dutch or English (depending on the lecturer), exercises and exam are in English. In the exercise classes both languages can be used.

Course Load

Total course load 5 EC = 140 hours, of which 44 hours are spent attending lectures and tutorials (11x2 hours lectures + 11x2 hours tutorials). Approximately 40 hours are needed to study the course material. The remaining 56 hours are spent on completing the assignments and preparing for and participating in the exam.

Assessment method

Written exam (closed book) with open questions.
The final grade is calculated using the grade of the exam and adding a bonus of maximally 1 point to be earned by handing in homework assignments. For the retake exam the bonus does not apply.

Reading list

David J. Griffiths and Darrell F. Schroeter, Introduction to Quantum Mechanics, 3rd edition, ISBN 978-1-107-18963-8 (hard back). This is the same book as used in the Quantum Mechanics 1 course. As complement to the textbook the lecture notes Quantum Statistical Physics will be made available.
Errata and a warning about incomplete international editions of the textbook can be found on the personal homepage of David Griffiths


From the academic year 2022-2023 on every student has to register for courses with the new enrollment tool MyStudyMap. There are two registration periods per year: registration for the fall semester opens in July and registration for the spring semester opens in December. Please see this page for more information.

Please note that it is compulsory to both preregister and confirm your participation for every exam and retake. Not being registered for a course means that you are not allowed to participate in the final exam of the course. Confirming your exam participation is possible until ten days before the exam.
Extensive FAQ's on MyStudymap can be found here.


Lecturer:Dr. M.P. Allan