## Admission requirements

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

## Description

The usefulness of quantum mechanics does not stop with the analytical solution of the Bohr model of the hydrogen atom. 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.

This comprises the study of indistinguishable quantum particles and their statistical distributions and the use of perturbation methods to understand the energy levels of atoms. The details of the observed emission spectrum of hydrogen are inconsistent with the Bohr model and simple analytical solutions of the Schrödinger equation. Most notably, the so called spin-orbit coupling gives rise to small shifts and splittings of the Bohr levels. The coupling of an atom to an external oscillating field gives rise to stimulated emission and can be understood in the framework of time-dependent perturbation theory.

The following topics are treated:

Quantum statistical description of indistinguishable particles

Fermi-Dirac, Bose-Einstein, and Planck distribution

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: entanglement, quantum computers, Dirac equation.

## 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

## Soft 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 exercise classes, working out exercises, and preparing for the exam.

## Timetable

## Mode of instruction

Lectures, tutorials (exercise classes) and homework assignments. The lectures are in Dutch, 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 42 hours are spent attending lectures and tutorials (11x2 hours lectures + 10x2 hours tutorials). Approximately 40 hours are needed to study the course material. The remaining 58 hours are spent on completing the assignments and preparing for 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.

## Blackboard

Course material is on Blackboard

To access Blackboard you need your ULCN-account Blackboard UL

## 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.

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

## Contact

Contact Details Lecturer:Dr.Peter Denteneer