Physik IV - Spring 2008

Prof. Andreas Wallraff




Atoms, photons, electrons, fundamentals of quantum mechanics, one dimensional problems, particle in box, tunneling, harmonic oscillator, hydrogen atom, spin, superposition and entanglement, quantum information, basic atomic physics, Zeeman effect, Stark effect, many electron atoms, molecules, quantum statistics, fermions, bosons, [basics of solid state and nuclear physics]


There will be a 120 minute written examination in Sessionsprüfung on 14.08.2008 at HPH G2 & HPH G3. There will also be an opportunity to repeat the exam in the following Sessionsprüfung.

Material allowed will be: A translation dictionary, an electronic calculator (also a programmable one!), and up to 10 sides (i.e. 5 two-sided pages) of handwritten notes.

Questions & Answers Session

The 'Questions & Answers' session to the topics covered in the lecture will take place Thursday, Aug 7, 10 am at HPM C 53.
Please send your questions some time in advance to () so that we can get prepared.


All classes begin 15 minutes earlier and finish 30 minutes earlier than indicated.

WhatStart DateDayTimeLocation
Lecture18.02.2008Monday1600-1700HPH G2
Lecture20.02.2008Wednesday1400-1600HPH G2
Exercises25.02.2008Monday1400-1600HPK D 24.2, HPP G3,G5,G6,G7,H1,H2,H5

Lecture Dates and Notes

1118.02.2008Organization of Class
220.02.2008Atomare Masseneinheiten, Avogadro-Konstante, Massenspektroskopie, Streuexperimente, Wirkungsquerschnitte, Atom-Volumen, Roentgenbeugung, Bragg-Streuung
2325.02.2008Abbildung von Atomen: Optisch, TEM, STM, Elektronstreuung, Alphastreuung
427.02.2008Rutherford-Streuung, Photoeffekt, Roentgenstrahlung, Compton-Effekt
3503.03.2008Compton-Wellenlaengenverschiebung, Temperaturstrahlung
605.03.20081D/3D Schwarze Strahler, Rayleigh-Jeans Gesetz, Plancksches Strahlungsgesetz, Wiensches Verschiebungsgesetz, Stefan-Boltzmann Gesetz, Elektronen-Ladung, Masse, Groesse, Welleneigenschaften, DeBroglie Wellenlaenge
4710.03.2008Materiewellen, Wellenpakete
812.03.2008Heisenberg'sche Unschaerferelation, Materiewellen am Doppelspalt, Welle-Teilchen Dualismus
5917.03.2008Spektren, Grundlagen des Bohr-Modells
1019.03.2008Bohr-Modell, Wasserstoff- und aehnliche Atome, Rydberg-Atome, Franck-Hertz Experiment
24.03.2008No lectureOsterferien
26.03.2008No lectureOsterferien
61131.03.2008Grundlagen der Quantenmechanik,1D Potentialtopf, Wellenfunktionen
1202.04.2008Schroedinger Gleichung, Operatoren, Erwartungswerte
71307.04.2008Messung, Eigenfunktionen, Eigenwerte, Kommutatoren, Superpositionsprinzip
1409.04.2008Endlicher Potentialtopf, Tunel-Effekt, Harmonischer Oszillator
814.04.2008No lectureSechseläuten
1516.04.2008Harmonischer Oszillator, Erzeugungs- und Vernichtungsoperatoren
91621.04.2008Wasserstoff-Atom, Drehimpuls
1723.04.2008Zeeman-Effekt, Separation der Variablen
101828.04.2008Loesungen der Schroedinger-Gleichung des Wasserstoff-Atoms und deren Visualisierung, Quantenzahlen
1930.04.2008Spin, Stern-Gerlach, Spin-Bahn Kopplung, Gesamtdrehimpuls
112005.05.2008Spektrum des Wasserstoff-Atoms
2107.05.2008Mehrelektronenatome, Pauli-Prinzip, Fermionen und Bosonen
1212.05.2008No lecturePfingsten
2214.05.2008Periodensystem, Schalen, Besetzung elektronischer Zustaende, LS-Kopplung, Termsymbole
132319.05.2008Spektren von Mehrlektronenatomen
2421.05.2008Auswahlregeln und Matrixelemente, charakteristische Roentegnstrahlung, Auger-Effekt, Molekuele, Rotationen, Schwingungen
142526.05.2008Molekuele, Kovalente Bindung, Rotationen, Schwingungen
2628.05.2008Wasserstoff-Molekuel, Hybridisierung, Fluoreszenz, Phosphoreszenz
Notizen Vorlesung 1-26
Folien Vorlesung 1-26

Additional Session: Quantum Mechanics on the Computer

When you will be working in an experimental lab or in a theory group later during your studies you will notice that many problems in quantum mechanics can not easily be solved analytically. In these cases it will be useful to be able to resort to numerical techniques for solving quantum mechanics problems. As part of the Physics IV lecture we will offer an introduction to solving and visualizing quantum mechanics problems on the computer.

Problems to be covered include:

The examples will be based on the Mathematica a software package available free of charge to ETH students at IDES.

You may want to start exploring the software by going to the help menu. In the Documentation Center you find tutorials such a "the first five minutes with ..." that help you to get to know the software. We will also provide some basic introduction during the "Quantum Mechanics on the Computer" classes. The class will take place roughly every second week on Mondays after the lecture. Additionally, in case of conflicting schedules there will be a smaller session after the lecture on Wednesdays in HPF G 6. Exercise problems will be provided.

QM on the Computer: Schedule and Files

103.03.2008Schwarzer Strahlersession1.nb,firas_monopole_spec_v1_mod.txt
307.04.2008Schroedinger Gleichungsession3.nb
428.04.2008Hydrogen Atomsession4.nb
426.05.2008Angular Momentum Additionsession5.nb


Exercise set answers will be done and handed in by groups of 3 students (or 2 if there is an even remainder). Groups will be organised in the first lecture session on Monday 18.02.2008. Each group's answers will be handed in on the dates shown below and given a mark each week out of 10. An overall score of 50% (50/100) will be required for Testat. Each student will also be required to present a solution individually in the exercise class three times during semester. A schedule for this will be organised in the first class.

Set 1Solutions 1
Set 2Solutions 2
Set 3Solutions 3
Set 4Solutions 4
Set 5Solutions 5
Set 6Solutions 6
Set 7Solutions 7
Set 8Solutions 8
Set 9Solutions 9
Set 10Solutions 10

Problem Set Schedule

DateTipsHand in/Present/DiscussHand back
25.02.2008Set 1
03.03.2008Set 2Set 1
10.03.2008Set 3Set 2Set 1
17.03.2008Set 4Set 3Set 2
24.03.2008No sessionOsterferien
31.03.2008Set 5Set 4Set 3
07.04.2008Set 6Set 5Set 4
14.04.2008No sessionSechseläuten
21.04.2008Set 7Set 6Set 5
28.04.2008Set 8Set 7Set 6
05.05.2008Set 9Set 8Set 7
12.05.2008No sessionPfingsten
19.05.2008Set 10Set 9Set 8
26.05.2008Set 10Set 9
Semester EndSet 10

Student presentations

There is a lot of interesting research going on at ETH and around the world that is related to the topics covered in this lecture course, and there will be also an opportunity for student groups to do a presentation on a novel piece of research, during the exercise classes. This will earn the presenting group an extra 10 points, to count towards their total mark out of 100.

You will be able to sign up to give a presentation after the lecture on Monday 21.04.2008. You can choose from the topics below. The TA who is named next to each topic will be able to answer any questions that you have about the topic while you prepare your presentation. The presentations will be given at the end of the exercise class on 05.05.2008 (and also on 19.05.2008 if there are many). The presentation will be given in the exercise class of the TA responsible for the topic, and if you are not giving a presentation you will be able to join the presentation that you are most interested in.

Possible topics

TopicDescriptionMaterialTeaching AssistantPresenter
Scanning Tunneling Microscope (STM) The Scanning Tunneling Microscope (STM) offers a powerful tool to study surfaces of solids with atomic resolution. The STM further offers the possibility to arrange atoms on a surface by using its tip as placing tool. L. Koenders, Physik in unserer Zeit 6 (1993) 260,
Binning et al., Phys. Rev. Lett. 49 (1982) 57
Martin GöpplC. von Duester
Transmission Electron Microscope (TEM) The TEM (transmission electron microscope) uses an electron beam passing through a very thin sample to create a very high resolution image. Invented in the 1930s it is now a very valuable tool in surface and material sciences due to sub angstrom resolution, allowing direct imaging of atoms in material formations. M. Varela et al., Phys. Rev. Lett 92 (2004) 095502 ,
E. M. James and N. D. Browning, Ultramicroscopy 78 (1999) 125
Bose-Einstein condensate (BEC) A Bose--Einstein condensate (BEC) is a state of matter ( very close to absolute zero ( (0 K or -273.15°C), where a large fraction of particles collectively occupy the lowest energy state and quantum effects become apparent on a macroscopic scale. Until its first realization in 1995 the experimental creation of a Bose-Einstein condensate was the holy grail in cold atom physics and required the development of new experimental techniques such as laser cooling and evaporative cooling. The talk should give a qualitative understanding of what Bose-Einstein condensation is, how it can be experimentally realized and discuss some basic properties of this new state of matter.
W. Ketterle, Physica Scripta (1996),
M. Anderson, Science 269 (1995) 198,
K. B. Davis, Phys. Rev. Lett. 75 (1995) 3969.
Torben MüllerA. Faisst, S. Thaler
Cavity quantum electrodynamics (cavity QED) Cavity quantum electrodynamics (cavity QED) studies the interaction of matter and light at its most fundamental level. The 'Cavity' in 'Cavity QED' typically refers to an optical or microwave resonator being employed, while 'QED' refers to the quantum nature of the coherent interactions between the material system (e.g. atoms) and the electromagnetic field (i.e. photons) confined inside the reflective cavity. Such an experimental setup draws its importance from the fact that it becomes possible to study matter-light interactions under circumstances in which their quantum nature is not totally 'washed out' by the influence of environmental noise ever present in the macroscopic world. Moreover it is possible to controllably create entanglement between atoms and photons thus providing a natural interface between flying qubits (photons) and stationary qubits which is crucial for quantum information processing and communication (QIPC). S. Haroche and J.-M. Raimond, Scientific American 4 (1993) 28
(german translation: Spektrum der Wissenschaft 6 (1993) 48),
H. Mabuchi et al., Science 298 (2002) 1372.
Johannes Fink
Atom Traps Traps for free charged and neutral particles without material walls permit the observation of isolated particles, even of a single one, over a long period of time and therefore according to Heisenberg's uncertainty principle enable us to measure their properties with extremely high accuracy. This paper is based on the presentation of the 1989 Nobel Prize in Physics by Wolfgang Paul. Basics of trapping charged and neutral particles are explained and short historical backgrounds of the development of the traps are given. W. Paul, Rev. Mod. Phys. 62 (1990) 531. Bruno Zimmerman
Quantum Dots Quantum dots might be one of the building blocks for a prospective quantum computer. However, research in this field was triggered only a little bit more than years ago. The first paper, written by two of the leading researchers in this field, gives a superficial introduction to the main and fascinating features of quantum dots. The second paper goes more into details, elaborating the issues mentioned in the previous paper like the different energy scales or the role of the spin. L. Kouwenhoven and C. Marcus, Physics World 6 (1998) 35,
L. Kouwenhoven, D.G. Austing and S. Tarucha, Rep. Prog. Phys. 64 (2001) 701.
Stephan Schnez
Vertical-cavity surface emitting laser (VCSEL) In 1964 Townes, Basov and Prokhorov were awarded the Nobel Prize in Physics "for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle." Already at that time semiconductors were singled out as one of the most promising materials for lasers1. Now-adays, microstructured semiconductor lasers are widely used in many applications and they exploit many concepts that you have studied in this class, e.g. the idea of using a quantum well as the gain medium2. The vertical-cavity surface emitting laser (VCSEL) belongs to this category of lasers3. In your presentation, you will describe the principle of operation of this device, how it is developed (methods and materials), and briefly describe a few applications. vcsel
Figure: Schematic of a VCSEL. (Inset: picture of what the device looks like after packaging
N. Basov, Nobel Lecture, December 11, 1964,
P. Gourley, Nature 371 (1994) 571,
K. Iga, IEEE Journal of selected topics in quantum electronics 6 (2000) 1077.
Dr. Valeria Liverini
Atomic Force Microscope (AFM) The atomic force microscope can investigate any kind of surface on an atomic scale. It uses mechanical springs to sense forces and piezoelectric transducers for scanning. It's main advantage compared to a scanning tunneling microscope is that it can characterize non conducting samples. G. Binning and C. F. Quate, Phys. Rev. Lett. 56 (1986) 930,
E. Meyer, Prog. Surf. Science 41 (1992) 3
Romeo Bianchetti / Peter Leek (only 19.05.2008)D. Ries, L. Bort

Testat Conditions

An overall mark of 50% (50/100) will be required in the exercises. An additional 10 points to count towards the total will be awarded to students (in groups of 2) who choose to do a presentation on a research topic. Students are also required to present an exercise solution twice during the semester.

Exercise Groups and Assistants

Dr. Peter Leek EN
Dr. Stefan Filipp DE,EN
Dr. Hakan Türeci EN
Teaching Assistants
Romeo Bianchetti IT,DE,ENHPK D 24.2
Johannes Fink DE,ENHPP G3
Martin Göppl DE,ENHPP G5
Dr. Valeria Liverini EN,ITHPP G6
Torben Müller DE,ENHPP G7
Gabriel Puebla-Hellmann DE,ENHPP H1
Stephan Schnez DE,ENHPP H2
Bruno Zimmerman DE,ENHPP H5

Suggested Reading

Physik IV course booksAuthorYear
Concepts of Modern Physics (McGraw-Hill)Beiser2003
The Physics of Atoms and Quanta (Springer)Haken, Wolf1993
Other introductory texts
Introduction to Quantum MechanicsPhilips2003
Quantum MechanicsRae2002
Quantum PhysicsGasiorowicz2003
Quantum MechanicsMerzbacher1998
Quantum MechanicsMessiah2000
Principles of Quantum MechanicsShankar1994
Books on special topics
Molekuelphysik und Quantenchemie (Springer)Haken, Wolf1994
Festkoerperphysik (Springer)Ibach, Lueth1990
Quantum Computation and Information (Cambridge)Nielsen, Chuang2000
Additional reading
In Search of Schrödinger's CatGribbin2002
Quantum Physics: Illusion or Reality?Rae2004

Past Course Notes

CourseLecture notes
Physik IV 2007 (Wallraff)
Physik IV 2006 (Lilly)pdf
Physik IV 2005 (Pescia)pdf

Past Examinations

Physik IV 2007 Final Exam (31.01.2008)pdf
Physik IV 2007 Final Exam (30.08.2007)pdf
Physik IV 2007 Mock Exam (20.06.2007)pdf
Physik IV 2007 Mock Exam Solutionspdf