# Tomi Johnson

# Tomi Johnson

Post-Doctoral Researcher and Lecturer at Keble College

**Research Fellow** at the Centre for Quantum Technologies, National University of Singapore**College Lecturer in Physics** at Keble College, University of Oxford

I am a theoretical physicist with a broad range of interests, from cold atomic gases and many body physics, to quantum information and computing, and methods for simulating non-equilibrium stochastic and quantum processes.

For more information, go to my homepage.

Students looking for information on a course I teach should expand the appropriate section below.

### CP3&4: Mathematical methods I&II

Here you will find some information regarding the organisation of tutorials and a few bits and pieces about the CP3&4: Mathematical methods I&II course. Please email if you have any questions about the work or anything else.

### CP3&4: Motivation

The laws of physics are astonishingly accurately described by the language of mathematics. Consequently, throughout your time as a physicist you will need familiarity with and understanding of a wide array of mathematical techniques.

At Oxford, we choose to teach you a large portion of these techniques in your first year. You will find yourself using many of them immediately in the first year course and the others soon after. The mathematics you learn this year will be the backbone of your physical knowledge, and a strong understanding of this course will support you through your undergraduate degree and beyond. Through first year electromagnetism, second year quantum mechanics, third year condensed matter, you will repeatedly return to techniques learnt in this module. Additionally, if you eventually leave the world of physics, the mathematics you learn here will be among the most transferable of the technical skills you will learn as an undergraduate.

Despite the many reasons above for studying mathematics, don't forget to enjoy its beauty for its own sake!

### CP3&4: Non-Keble-specific course information

Much of the information you need about the course is given in the lecture course materials and undergraduate handbook. Specifically, seek information about the lectures on 'Complex Numbers and Ordinary Differential Equations' by Prof. J. Yeomans, 'Vectors and Matrices' by Prof. A. Lukas and 'Calculus' by Dr. A. Slyz, and about the CP3 and CP4 modules.

You will find syllabi, recommended reading material, lecture notes, and the lecturers' problem sets (note that I will set different problems to the lecturers' - see below - but the lecturers' problems are still as relevant and useful). If you ask previous years, you might also be able to find previous problem sets and lecture notes, and be recommended other reading. The more problems you answer and the more perspectives you get on the subject, the better.

When it gets closer to your examinations, I can't emphasise enough how important it is to work through past exam papers; it's by far the easiest way to improve your grade. The first year mathematics course hasn't changed much over time, so there are many relevant questions available. To find some, go here. Also, you should gain familiarity with the data sheet with which you will be provided for your exams.

### CP3&4: Keble-specific course information

#### Tutorials and problem sets - procedure

A tutorial session starts at 2pm with a class of approximately 1.5-2 hours duration. This is followed by paired tutorials of 30 minutes each (the order of pairs does not need to be decided in advance, it can be decided by you at the end of the class).

Written solutions with accompanying cover sheet (see below) are submitted in advance of each tutorial session, returned at the beginning of each class, and required for the paired tutorials. Please hand in all written work by 5pm two days before the tutorial (except for tutorials on a Monday where the deadline is the Friday of the previous week at 5pm). Vacation work is to be submitted by 5pm on Thursday of 0th week.

For revision sessions or when returning vacation work only, there are no paired tutorials.

Important:

- The problem sets are my own
*not*the lecturers' (they are given below). - You only need to submit written answers to the 'Problems'
*not*the 'Class problems'. You will be asked individually or as a group to solve a selection of the Class problems during the class and/or tutorial, and so you may, at least, wish to look at them in advance.

#### Tutorials and problem sets - aims

The general aims of physics tutorial sessions and problem sets are discussed here.

The aims of the mathematical methods tutorial sessions and the solving of the corresponding problem sets are (i) to learn how to efficiently apply mathematical methods in solving physical and mathematical problems; (ii) to learn how to produce answers that discuss the approach taken by the solver and explain (using an appropriate mix of mathematics, English and diagrams) how mathematical tools were employed in obtaining solutions; (iii) to start appreciating how and why mathematics is an important tool for describing and discussing physical arguments; and (iv) to learn how to acquire new mathematical skills in self-study for approaching advanced physics problems.

The goals for each session are listed in the problem sets.

While I will mark your work and assess you to ensure that no-one is falling behind, the aim of the tutorials and problem sets is *not* to fool me into believing that you understand more than you know. In fact, it is the opposite. It is an opportunity for you to present your state of understanding to me as honestly as possible, such that I have the best chance of adding to it, and to ask me as many questions as possible.

As such, each piece of written work that is handed in must be accompanied by a short self-assessment (usually on the cover page) of how well you have achieved the established goals while preparing for the tutorial session, any issues you may have encountered with problems, and any other difficulties you are having with or questions you have about the topic. Also, please be bold enough to raise such issues directly in the class or paired tutorial. Instead of directing me away from your weaknesses, direct me towards them so that we can overcome them.

Another common mistake is to see your Keble physics year group as competition rather than a support network. While you will be directly competing against them in your all-important University examinations, it is not the best strategy to act competitively throughout the year. For a simple calculation, assume you only need to compare yourself against the mean mark of the *n* students in your University physics year group. Then for it to be beneficial for you to assist your peer such that their score is raised by *x%*, all you need to receive in return is *(x/n)%*. Remember that *n* is approximately 180. Therefore, go to your Keble physics year group for help, talk through problems you are having together, share resources and information, and approaches to answering tutorial and past paper problems, assist another who asks for your help. It is often the year group that works together that goes on to get the best results. In previous years, whiteboards were made available to help with group discussions, please ask me if you want one. (Of course, unthinkingly copying another students solutions will be obvious and beneficial to no-one in the long term.)

#### Books

All of the following recommended books are available in the Keble physics book loan scheme:

- "Mathematical Methods for Physics and Engineering: A Comprehensive Guide" K.F. Riley, M.P. Hobson, S.J. Bence (RHB)
- "Mathematical Methods in the Physical Sciences" M.L. Boas (MLB)
- "All You Wanted to Know about Mathematics But Were Afraid to Ask" L. Lyons (LL)
- "Mathematical Methods for Science Students" G. Stephenson (GS)
- "Vibrations & Waves" A.P. French (FR)
- "Waves - Berkeley Physics Course" F.S. Crawford (C)

The book RHB is a good source of information for the mathematics tutorials starting at a basic level and covering a broad range of important mathematics topics covered in the course. I suggest this as the main book for the course and primary source of information for self-study. The problem sets list a small subset of those chapters of the books that should be read in preparation for the corresponding tutorial. Reading these chapters may help you solve the tutorial problems. However, the primary motivation for studying them should be to gain additional insights into mathematics and getting a broader and/or alternative view on topics covered in the course. There are many books than the above in the library that could be of use and interest!

Note: For the topic of waves, students of previous years have additionally found a book by D. J. Morin (available only in electronic draft form here) to be useful.

#### Mathematica

At Keble, we particularly encourage students to use the symbolic computer algebra software Mathematica to aid their studies. Mathematica is an excellent tool for checking answers and gaining deeper insights into the structure of answers through its visualisation capabilities. It can solve most of the problems posed on the problem sets. However, the program is only a study aid; students are still required to solve problems using pen and paper, Mathematica printouts handed in as written tutorial work are not acceptable.

Please go to here for information about how to obtain the Mathematica kit and license. Also, the website Wolfram Alpha, which is based on Mathematica, is an excellent resource for learning and using symbolic computer algebra programs.

### CP3&4: Tutorial schedule

I will keep you updated with when and where tutorials sessions will be and when to hand in work, but it might be useful to check the following list which I will keep up to date. Email me if there is any ambiguity.

As you answer the problems, you may wish to refer to and become familiar with the data sheet with which you will be provided in your exams. Note, however, it is entirely fair for examiners to ask you to derive many of the identities appearing on the sheet and you should wish to understand their origin/reproduce their derivation as with any of the other identities to which you will be introduced in the course. The aim of telling you about the sheet now is to get you familiar with it, so you are able to use it at speed to answer an exam question that uses the identity without asking for its derivation.

#### MT Week 1

Topics covered: Vacation work and complex numbers.

Problems: Vacation problem set and tutorial sheet 1.

Hand in work: Thursday 0th week 5pm (vacation work) or Monday 1st week 5pm (tutorial sheet 1), Keble lodge.

Class: Wednesday 1st week 2-4pm, location Seminar Room 6.

Tutorials: Wednesday 1st week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### MT Week 2

Topics covered: Calculus I.

Problems: Tutorial sheet 2.

Hand in work: Friday 1st week 5pm, Keble lodge.

Class: Tuesday 2nd week 2-4pm, location Seminar Room 2.

Tutorials: Tuesday 2nd week 4pm onwards, Dieter Jaksch's office (Room 3803).

Topics covered: Vectors and matrices I.

Problems: Tutorial sheet 3.

Hand in work: Monday 2nd week 5pm, Keble lodge.

Class: Wednesday 2nd week 2-4pm, location Seminar Room 6.

Tutorials: Wednesday 2nd week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### MT Week 3

Topics covered: Calculus II.

Problems: Tutorial sheet 4.

Hand in work: Monday 3rd week 5pm, Keble lodge.

Class: Wednesday 3rd week 2-4pm, location Seminar Room 6.

Tutorials: Wednesday 3rd week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### MT Week 4

Topics covered: Vectors and matrices II.

Problems: Tutorial sheet 5.

Hand in work: Monday 4th week 5pm, Keble lodge.

Class: Wednesday 4th week 2-4pm, location Seminar Room 6.

Tutorials: Wednesday 4th week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### MT Week 5

Topics covered: Ordinary differential equations.

Problems: Tutorial sheet 6.

Hand in work: Monday 5th week 5pm, Keble lodge.

Class: Wednesday 5th week 2-4pm, location Seminar Room 6.

Tutorials: Wednesday 5th week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### MT Week 7

Topics covered: Advanced problems.

Problems: Tutorial sheet 7.

Hand in work: Monday 7th week 5pm, Keble lodge.

Class: Wednesday 7th week 2-4pm, location Seminar Room 6.

Tutorials: Wednesday 7th week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### Christmas vacation

Topics covered: Assorted.

Problems: Christmas vacation problems.

#### HT Week 1

Topics covered: Damped harmonic oscillator, vacation work and College exam.

Problems: Christmas vacation problems, tutorial sheet 1, and the College exam paper.

Hand in work: Thursday 0th week 5pm (vacation work) and Monday 1st week 5pm (Tutorial sheet 1), Keble lodge.

Class: Tuesday 1st week 2-4pm, Seminar Room 1.

Tutorials: Tuesday 1st week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### HT Week 2

Topics covered: Multiple integrals and vector calculus.

Problems: Tutorial sheet 2.

Hand in work: Monday 2nd week 5pm, Keble lodge.

Class: Wednesday 2nd week 2-4pm, Seminar Room 6.

Tutorials: Wednesday 2nd week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### HT Week 3

Topics covered: Waves and normal modes.

Problems: Tutorial sheet 3.

Notes: Notes on waves and normal modes.

Hand in work: Monday 3rd week 5pm, Keble lodge.

Class: Wednesday 3rd week 2-4pm, Roy Griffiths Room.

Tutorials: Wednesday 3rd week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### HT Week 5

Topics covered: Multiple integrals and vector calculus II.

Problems: Tutorial sheet 4.

Notes: Notes on curvilinear coordinates.

Hand in work: Monday 5th week 5pm, Keble lodge.

Class: Wednesday 5th week 2-4pm, Seminar Room 6.

Tutorials: Wednesday 5th week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### HT Week 6

Topics covered: Waves and normal modes II.

Problems: Tutorial sheet 5.

Notes: Notes on waves and normal modes.

Hand in work: Monday 6th week 5pm, Keble lodge.

Class: Wednesday 6th week 2-4pm, Roy Griffiths Room.

Tutorials: Wednesday 6th week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### HT Week 8

Topics covered: Advanced problems.

Problems: Tutorial sheet 6.

Hand in work: Monday 8th week 5pm, Keble lodge.

Class: Wednesday 8th week 2-4pm, Seminar Room 6.

Tutorials: Wednesday 8th week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### Easter vacation

Topics covered: Assorted.

Problems: Easter vacation problems.

#### TT Week 1

Topics covered: Vacation work and College exams.

Problems: Easter vacation problems and the College exam paper.

Hand in work: Thursday 0th week 5pm (vacation work), Keble lodge.

Class: Tuesday 1st week 2-4pm, Jean Robinson room.

Tutorials: Tuesday 1st week 4pm onwards, Dieter Jaksch's office (Room 3803).

#### TT Week 2

Topics covered: Vacation work and College exams (again).

Problems: Easter vacation problems and the College exam paper.

Hand in work: Thursday 0th week 5pm (vacation work), Keble lodge.

Class: Monday 2nd week 2-4pm, Seminar Room 1.

Tutorials: Monday 2nd week 4pm onwards, Dieter Jaksch's office (Room 3803).

### BIII: Quantum, atomic and molecular physics

Here you'll find some information regarding the organisation of tutorials and a few bits and pieces about the BIII: Quantum, atomic and molecular physics course. Email if you have any questions about the work or anything else.

### BIII: Motivation

The first two years of the Oxford physics course have given you a great introduction to the key mathematical methods and physical principles that underlie the various diverse options you'll be taking in your third and fourth years. You'll be studying the very large: comparing cosmological models and dealing with large complex astrophysical and atmospheric systems. In B2 we'll work at the other end of the spectrum, the very small: subatomic particles, nuclei, atoms and molecules. Whereas the physics of the very large doesn't necessarily affect the way we look at the small, the physics of the small certainly plays a big role in physics. Particle physics can tell us much about the early seconds of the universe and the ionisation energy of hydrogen is important to many of the cosmological models you'll be learning about. Similarly, nuclear physics explains how stars power themselves, avoid collapse, and why stars go through the phases they do. The greenhouse effect all rests on the energy levels of molecules such as CO_{2} and methane CH_{4}, while much of solid state physics relies on understanding the atoms making up the crystal lattice.

B2 begins by looking at atoms, since the internal structure of nuclei and subatomic particles only affect atomic behaviour in a small way, and atomic physics provides a well understood and structured application of the quantum mechanics you learned in your second year. In BIII we'll gain a detailed understanding of the energy levels of atoms and see how this changes when they bond to form molecules. Atoms don't exist in isolation and we'll focus on how they interact with the electromagnetic field. The motivation for this is two-fold: the interaction between the electromagnetic field and matter is the way we manipulate and learn about matter, and the ability to exploit this interaction to create a laser is used in a huge range of devices, from DVD players to quantum computers.

Finally, I personally quite like atomic physics because the history of the subject is very closely related to the history of quantum mechanics itself. For instance, quantum mechanics developed from theories like the Bohr model of the atom and a need to understand atomic spectra. Einstein and Dirac's insights made during the 1910s and 20s still form the basis of how we'll deal with the interaction of light and matter in this course. It is also a very precise subject with relatively little handwaving and a clear structure covered by many good text books, which might suit many of you.

### BIII: Course material

Most of the course materials can be accessed from the department website but I've collected together the relevant bits below.

*Syllabus*: Oxford physics syllabuses and synopsises tend to be a bit on the vague side but I've attached links to them below. Since the syllabus has recently changed it might be wise to partially use the lecture course as a guide to what is likely to be examined.

>> Syllabus and synopsis (pp. 7-8)

*Notes*: The recommended atomic physics lecture notes are those by Paul Ewart and the molecular/laser part will be taught by Simon Hooker, who has written his own lecture notes as well as a book on the topic.

>> Paul Ewart's notes and slides

>> Simon Hooker's notes on molecules and lasers

>> Simon Hooker's book on lasers

*Problem sets*: The atomic physics problem sets are from Derek Stacey's 2005 course. They're a little offset from the current syllabus, for example, the introductory problem set assumes you looked at spin-orbit coupling and fine structure in the A3 course, but you should be able to deal with this. The other parts of the course have problem sets specifically written for them.

>> Derek Stacey's problems

>> Problem sets 3, 4 and 5

*Reading*: The link to the course reading list is given below. For atomic physics, my personal recommendation is Woodgate's book as it is concise yet rigorous, however, the concepts might be easier understood using Chris Foot's book. The key text for molecules is that by Bransden and Joachain. Simon Hooker's book and lecture notes will contain everything you need to know for the lasers part of the course. You may feel the need to recap some of last year's A3 course and any of Gasiorowicz, Shankar or Binney's books are good for this (the latter is published online and I've provided a link).

>> Reading list

>> PDF of Binney's book

#### Examination material

I can't emphasise enough how important working through past exam papers is; it's by far the easiest way to improve your grade. As they have changed the syllabus recently the relevant past examination questions are a bit trickier to find. They have provided a sample paper which I've provided a link to. The previous syllabus had an almost identical atomic physics course leading to the B1 exam and so questions 1 and 2 from B1 past papers of 2004-2010 are good practice. For the other parts of the course the lectures have made a list of relevant past paper questions.

>> Past examination papers

>> Sample problems

>> Sample exam papers

>> List of relevant past paper questions

#### Additional links

Since the topics taught as part of this course are well established you can find a plethora of atomic and laser physics lecture notes from a quick google search. These might provide another way of looking at a topic if you're not satisfied with the other explanations. I've linked to two examples here.

>> Mark Fox's lecture notes

>> W. Johnson's book (advanced!)

### BIII: Tutorial schedule

I'll keep you updated with when and where tutorials will be and when to hand in work, but it might be useful to check the following list which I'll keep up to date.

#### MT Week 1

Topics covered: Revision of hydrogen and helium

Problems: Questions 1-8 from Derek Stacey's problem set

Hand in work: Monday 10th October 5pm, "J" pigeon hole in the Clarendon lab

Tutorial: Wednesday 12th October 3-6pm

Where: Patrick Irwin's office in St Anne's

Pairings: TE and KH 3-4pm, BY and TV 4-5pm, ZW 5-6pm

#### MT Week 3

Topics covered: Central field, alkalis, LS coupling, spin-orbit interaction

Problems: Questions 9-14 from Derek Stacey's problem set

Hand in work: Monday 24th October 5pm, "J" pigeon hole in the Clarendon lab

Tutorial: Wednesday 26th October 3-6pm

Where: Patrick Irwin's office in St Anne's

Pairings: TE and KH 3-4pm, BY and TV 4-5pm, ZW 5-6pm

#### MT Week 4

Topics covered: Selection rules, hyperfine structure, atoms in magnetic fields, X-rays

Problems: Questions 15-20, 22 and 23 from Derek Stacey's problem set

Hand in work: Monday 31st October 5pm, "J" pigeon hole in the Clarendon lab

Tutorial: Wednesday 2nd November 3-6pm

Where: Patrick Irwin's office in St Anne's

Pairings: TE and KH 3-4pm, BY and TV 4-5pm, ZW 5-6pm

#### MT Week 5

Topics covered: Einstein relations, Rabi oscillations, Bloch sphere, density matrices

Problems: Problem set 3

Hand in work: Monday 7th November 5pm, "J" pigeon hole in the Clarendon lab

Tutorial: Wednesday 9th November 3-6pm

Where: Patrick Irwin's office in St Anne's

Pairings: TE and KH 3-4pm, BY and TV 4-5pm, ZW 5-6pm

#### MT Week 6

Topics covered: Molecular physics

Problems: Problem set 4

Hand in work: Monday 14th November 5pm, "J" pigeon hole in the Clarendon lab

Tutorial: Tuesday 15th November 3-6pm

Where: Neville Harnew's office in St Anne's

Pairings: TE and KH 3-4pm, BY and TV 4-5pm, ZW 5-6pm

#### MT Week 8

Topics covered: Lasers

Problems: Problem set 5

Hand in work: Monday 28th November 5pm, "J" pigeon hole in the Clarendon lab

Tutorial: Wednesday 30th November 3-6pm

Where: Patrick Irwin's office in St Anne's

Pairings: TE and KH 3-4pm, ZW 4-5pm, BY and TV 5-6pm

#### HT Collection Class

Class: Thursday, Week 1, 19th January 3-5pm

Where: Neville Harnew's office in St Anne's

#### TT Revision Class I

Class: Wednesday, Week 1, 25th April 3-6pm

Problems: Sample exam paper

Hand in work: Monday 23rd April 5pm, "J" pigeon hole in the Clarendon lab

Where: Neville Harnew's office in St Anne's

#### TT Revision Class II

Class: Tuesday, Week 3, 8th May 3-6pm

Problems: Sent out by email

Hand in work: Monday 7th May noon, "J" pigeon hole in the Clarendon lab

Where: Neville Harnew's office in St Anne's

### BVI: Condensed matter physics

Here you'll find some information regarding the organisation of tutorials and a few bits and pieces about the BVI: Condensed matter physics course. Email if you have any questions about the work or anything else.

### BVI: Motivation

Before starting the condensed matter physics course you will have already tackled atomic physics and seen that things get quite a bit more complicated when combining a few to form a molecule. The aim of a condensed matter course, to describe collections of ~10^{23} atoms, might then seem a little daunting. Looking around, you'll also realise that just within solids there is a huge variety of different types and properties to explain - "this is going to be nightmare", I hear you think.

It's a testament to the beauty of solid state physics that we can get handle these systems, explaining a huge array of features with (comparatively) very simple models. In some ways, as well as introducing you to the properties of solids, this course is a lesson in analytical physics; how to start with the most basic models and improve on them assumption by assumption.

While the foundations of the subject are now well known, a large proportion of current physics research is still done in this area, making it an important topic for anyone planning to stay in physics.

### BVI: Course material

Most of the course materials can be accessed from the department website but I've collected together the relevant bits below.

*Syllabus*: Oxford physics syllabuses tend to be a bit on the vague side but I've attached a link to this course's below. Since the syllabus has recently changed it might be wise to partially use the lecture course as a guide to what is likely to be examined.

>> Syllabus

*Notes*: The lecturer has written some very nice notes on the subject of the course, linked to below. My predecessor Tom Ouldridge also wrote brief notes on three topics, which I've linked to below, and I've added some notes of my own.

>> Steve Simon's notes.

>> Tom Ouldridge's notes on scattering, phonons and band theory.

>> My notes on holes.

*Problem sets*: We'll be working from problem sets linked to in the tutorial schedule below, not the ones provided by the lecturer. These are largely based on problems designed by Steve Simon, Tom Ouldridge and Gareth Alexander. Steve Simon's problem sets do provide some additional questions, which you can use during revision, as do Gareth Alexander's, so I've linked to these below.

>> Steve Simon's problem sets: 1, 2, 3, 4, 5, revision, and additional.

>> Gareth Alexander's problem sets: lattice structure; lattice dynamics; free and nearly free electrons; tight binding and semiconductors; magnetism.

*Reading*: The link to the course reading list is given below. I recommending you use Hook and Hall, Kittel, and Ashcroft and Mermin. Kittel is sometimes a bit too handwaving, while Ashcroft and Mermin gives a very comprehensive but advanced description of the topics, though is still quite readable. Hook and Hall provides a nice middle ground.

#### Examination material

I can't emphasise enough how important working through past exam papers is; it's by far the easiest way to improve your grade. As they have changed the syllabus recently the relevant past examination questions are a bit trickier to find, but look at B2 exams before 2011 along with A4/B3 exams before 2004/2005. Ignore questions on photonics, device physics, superconductivity, and symmetries. Other than that, most questions should be fair game.

>> Past examination papers

>> Sample exam and solutions

#### Additional resources

Since the topics taught as part of this course are well established you can find a plethora of condensed matter physics lecture notes from a quick google search. These might provide another way of looking at a topic if you're not satisfied with the other explanations. For example:

>> Britney Spears' guide to semiconductor physics.

### BVI: Tutorial schedule

I'll keep you updated with when and where tutorials will be and when to hand in work, but it might be useful to check the following list which I'll keep up to date.

#### HT Week 2

Topics covered: Solid state without the microscopic structure.

Problems: Tutorial sheet 1.

Hand in work: Monday 21st January 5pm, "J" pigeon hole in the Clarendon lab.

Class: Wednesday 23rd January 2-4pm, venue tbc.

Tutorials: Wednesday 23rd January 4-6pm, Dieter Jaksch's office.

#### HT Week 4

Topics covered: Lattices and scattering.

Problems: Tutorial sheet 2.

Hand in work: Monday 4th February 5pm, "J" pigeon hole in the Clarendon lab.

Class: Wednesday 6th February 2-4pm, Seminar Room 6.

Tutorials: Wednesday 6th February 4-6pm, Dieter Jaksch's office.

Relevant notes: Tom Ouldridge's notes on scattering.

#### HT Week 5

Topics covered: Bonding, phonons and expansion.

Problems: Tutorial sheet 3.

Hand in work: Monday 11th February 5pm, "J" pigeon hole in the Clarendon lab.

Class: Wednesday 13th February 2-4pm, Seminar Room 6.

Tutorials: Wednesday 13th February 4-6pm, Dieter Jaksch's office.

Relevant notes: Tom Ouldridge's notes on phonons.

#### HT Week 7

Topics covered: Nearly free electrons, tight binding model and semiconductors.

Problems: Tutorial sheet 4.

Hand in work: Monday 25th February 5pm, "J" pigeon hole in the Clarendon lab.

Class: Wednesday 27th February 2-4pm, Seminar Room 6.

Tutorials: Wednesday 27th February 4-6pm, Dieter Jaksch's office.

Relevant notes: Tom Ouldridge's notes on band theory, and my notes on holes.

#### HT Week 8

Topics covered: Magnetism.

Problems: Tutorial sheet 5.

Hand in work: Monday 3rd March 5pm, "J" pigeon hole in the Clarendon lab.

Class: Wednesday 5th March 2-4pm, Seminar Room 6.

Tutorials: Wednesday 5th March 4-6pm, Dieter Jaksch's office.

#### Revision week class

Topics covered: Everything.

Problems: tbc (no need to prepare anything before).

Class: Thursday 14th March 9am-12pm.

#### TT collection class

Topics covered: The collection.

Class: venue and time tbc