## Admission requirements

Quantum Mechanics 1, Classical Mechanics B, AN3na, LA2na

## Description

This courses deepens the understanding of quantum mechanics by studying important quantum phenomena and applications of quantum mechanics. This comprises the study of indistinguishable quantum particles and their statistical distributions and the use of perturbation methods to understand the level structure 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 ground state of Helium and simple molecules will be discussed using the variational principle.

## Course objectives

After the course the student should be familiar with the following concepts and should be able to apply these concepts to perform simple calculations.

• Quantum statistical description of indistinguishable particles

• Fermi-Dirac, Bose-Einstein and Planck distribution

• Understanding of the strucuture of atoms and periodic table using hydrogen orbitals

• Density of states

• Time-independent perturbation theory

• Fine-structure and hyperfinestructure of Hydrogen

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

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

• Stimulated and spontaneous emission, Einstein A and B coefficeints, selection rules

• Variational principle: ground state of Helium and covalent bond

In addition the student is introduced tot he following concept

• Dirac equation

• Adiabatic principle

• Geometrical phase and the Aharonov-Bohm effect

## Timetable

## Mode of instruction

Lectures, tutorials (exercise classes) and homework assignments

## 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 50 hoursare needed to study the course material. The remiang 48 hours are spent on completing the assignments and preparing for the exam

## Assessment method

Written exam with open questions.

The final grade is calculated using the grade of the exam and adding a bonus based on the homework assignments. To participate in the bonus all of the five homework assignments should be handed in. A final grade below 6 will be rounded to 5 if the grade for the written exam is insufficient (below 5.5).

There is an opportunity to re-take the exam. In this case no bonus applies.

## Blackboard

Course material is on blackboard

To access Blackboard you need your ULCN-account Blackboard UL

## Reading list

David J. Grifiths, Introduction to Quantum Mechanics, 2nd edition, ISBN 0-13-191175-9. 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 Divid Griffiths http://www.reed.edu/physics/faculty/griffiths.html

## Contact

Contactgegevens Docent:Dr. M. de Dood (Michiel)