## Admission requirements

Prior knowledge of Quantum Mechanics 1, Statistical Physics 1, Classical Mechanics B, Analysis 3 NA, Linear Algebra 2 (NA)

## Description

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

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.

## Timetable

Schedule

For detailed information go to Timetable in Brightspace

In MyTimetable, you can find all course and programme schedules, allowing you to create your personal timetable. Activities for which you have enrolled via MyStudyMap will automatically appear in your timetable.

Additionally, you can easily link MyTimetable to a calendar app on your phone, and schedule changes will be automatically updated in your calendar. You can also choose to receive email notifications about schedule changes. You can enable notifications in Settings after logging in.

Questions? Watch the video, read the instructions, or contact the ISSC helpdesk.

**Note:** Joint Degree students from Leiden/Delft need to combine information from both the Leiden and Delft MyTimetables to see a complete schedule. This video explains how to do it.

## 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 http://www.reed.edu/physics/faculty/griffiths.html

## Registration

As a student, you are responsible for enrolling on time through MyStudyMap.

In this short video, you can see step-by-step how to enrol for courses in MyStudyMap.

Extensive information about the operation of MyStudyMap can be found here.

There are two enrolment periods per year:

Enrolment for the fall opens in July

Enrolment for the spring opens in December

See this page for more information about deadlines and enrolling for courses and exams.

**Note:**

It is mandatory to enrol for all activities of a course that you are going to follow.

Your enrolment is only complete when you submit your course planning in the ‘Ready for enrolment’ tab by clicking ‘Send’.

Not being enrolled for an exam/resit means that you are not allowed to participate in the exam/resit.

## Contact

Lecturer:Dr. D.F.E. Samtleben

## Remarks

**Software**

Starting from the 2024/2025 academic year, the Faculty of Science will use the software distribution platform Academic Software. Through this platform, you can access the software needed for specific courses in your studies. For some software, your laptop must meet certain system requirements, which will be specified with the software. It is important to install the software before the start of the course. More information about the laptop requirements can be found on the student website.