The quantum world
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| 4 Tutor-marked assignments (TMAs) | 6 Interactive computer-marked assignments (iCMAs) |
| Examination | No residential school |
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Summary
If you're interested in the fundamental laws of modern physics and how mathematics is used to state and apply these laws, this course is for you. It surveys the physical principles, mathematical techniques and interpretation of quantum theory. The Schrödinger equation, the uncertainty principle, the exclusion principle, fermions and bosons, measurement probabilities, entanglement, perturbation theory and transition rates are all discussed. Applications include atoms, molecules, nuclei, solids, scanning tunnelling microscopy and quantum cryptography. The course also presents recent evidence relating to some of the most surprising and non-classical predictions of quantum mechanics.
Course content
Quantum mechanics is famous for challenging our intuitive view of the world. However, it does not simply frustrate classical mechanics: it replaces it by a clear and precise formalism and a set of principles that allow exact calculations to be made. This puts the subject in a unique position. Whilst it challenges our intuitions, it provides the concepts and quantitative predictions needed by applied physicists, chemists and technologists who wish to interpret and control phenomena on the nanoscale and below.
This course will give you a detailed understanding of the physical principles and mathematical techniques of quantum mechanics. Building on this understanding, you’ll learn about the interpretation of quantum mechanics in the light of recent experiments and discover how quantum mechanics is used to explain the behaviour of physical systems, from nuclei and atoms to molecules and solids.
The course materials include three books, accompanied by DVD-ROMs containing computer-based activities and video materials.
Book 1, Wave Mechanics, begins with a wide-ranging introduction to the quantum revolution. It then develops Schrödinger’s equation, together with the concepts of wave functions, expectation values and uncertainties. Schrödinger’s equation is solved for simple model systems such as particles in boxes and harmonic oscillators. You will also learn how the equation can be used in various applications including quantum dots and vibrating molecules. The concept of a wavepacket is introduced and used to describe the classical limit of quantum mechanics. Finally, the quantum processes of tunneling, barrier penetration and reflection are discussed, together with their application to nuclear fusion, alpha decay, and the scanning tunneling microscope. The mathematical techniques used and developed in this book include complex numbers, separation of variables, integration, differential equations and eigenvalues.
Book 2, Quantum mechanics and its interpretation, gives a more general discussion of quantum mechanical principles. It shows how quantum states can be represented by vectors in a vector space, with observable quantities represented by operators acting on the vectors. This formalism is used to derive quantum mechanical conservation laws and to provide a proof of the uncertainty principle. The properties of orbital and spin angular momentum are introduced and the extraordinary properties of systems of identical particles, including Bose-Einstein condensation, are explored. The book then discusses some fascinating topics in the interpretation of quantum mechanics, supported by the results of recent experiments. The process of measurement in quantum mechanics cannot be described by Schrödinger’s equation and appears to involve chance in an unavoidable way. The book ends by discussing the concept of entanglement, and its applications to quantum encryption and quantum teleportation. The mathematical techniques used and developed in this book include vector spaces, Hermitian operators and matrix algebra.
Book 3, The Quantum Mechanics of Matter shows how quantum mechanical methods are used to explain the behaviour of matter, from the scale of nuclei and atoms to molecules and solids. The hydrogen atom is discussed in detail, as well as hydrogen-like systems such as positronium. The useful technique of perturbation theory is developed to obtain approximate results in cases where exact calculations become difficult. The book goes on to discuss multi-electron atoms and the Periodic Table, molecular binding and the behaviour of electrons in the energy bands of metals, insulators and semiconductors. Finally, the book considers the interaction of matter with light. You will see how quantum mechanics can predict the lifetimes of atomic states and the brightness of spectral lines.
You will learn
In this course, you will learn the fundamental principles of quantum mechanics and the mathematical techniques needed to state and apply them. You will explore the interpretation of quantum mechanics and critically evaluate the extent to which quantum mechanics has been tested by experiment. You will also see how quantum mechanical methods are used to model phenomena in physical systems including atoms, molecules and solids.
Entry
This is a Level 3 course that builds on study skills and subject knowledge acquired from previous studies at Levels 1 and 2. It is intended for students who have recent experience of higher education in a related subject at this level.
The recommended prerequisite OU courses for studying SM358 are Mathematical methods and models (MST209) and The physical world (S207). The mathematical prerequisite is especially important, as it would be difficult to study SM358 without the necessary mathematical background. The parts of MST209 relating to ordinary and partial differential equations, matrices and angular momentum are especially important. S207 is the ideal physics course to prepare you for studying SM358 especially parts relating to classical and quantum mechanics.
It is essential that you establish whether or not your background and experience give you a sound basis on which to tackle SM358. The Science Faculty has produced a booklet Are You Ready For SM358? To help you decide whether you already have the recommended background knowledge and experience to start the course or whether you need some extra preparation. This can be viewed or printed from the Science Faculty website.
If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
Preparatory work
Since the course builds on Mathematical methods and models (MST209) and The physical world (S207), we recommend that you revise the relevant parts of these courses in the months before you start to study SM358. This is particularly important if it is some time since you studied these courses, or if the Are You Ready For SM358? booklet indicates that there are gaps in your knowledge or skills. This booklet also gives advice on the relevant topics to revise.
Qualifications
SM358 is an optional course in our:
- BSc (Honours) Natural Sciences (B16)
- BSc (Honours) Physical Science (B27)
- BA/BSc (Honours) Computing and Mathematical Sciences (B14)
- BA/BSc (Honours) Mathematics (B31)
- BSc (Honours) Mathematics and its Learning (B46)
- BSc (Honours) Secondary Education in Physics (B56)
- Diploma in Natural Sciences (D47)
- Diploma in Physical Science (E04)
It can also count towards most of our other degrees at bachelors level, where it can help to weight your degree towards a BSc.
We advise you to refer to the relevant qualification descriptions for information on the circumstances in which this course can count towards these qualifications because from time to time the structure and requirements may change.
Excluded combinations
Sometimes you will not be able to count a course towards a qualification if you have already taken another course with similar content. To check any excluded combinations relating to this course, visit our excluded combination finder or check with our Student Registration & Enquiry Service before registering.
If you have a disability or additional requirement
The course contains a large number of detailed equations. If you have severely impaired sight, you might find these aspects of the course challenging. It also contains coloured diagrams and uses computer software. The books are available in a comb-bound format.
If you are a new student, or new to courses using a computer or the internet, you will need to inform us of your particular needs as soon as possible, as some of our support services may take several weeks to arrange. Details of how to do this and our range of support services are described in our booklet Meeting your needs which you can download or request from our Student Registration & Enquiry Service.
You can also find information about accessible course materials, financial support and the Disabled Students' Allowance, equipment and other services, on our Services for disabled students website. It also includes our contact details for advice and support both before you register and while you are studying.
Course materials
What's included
Course books, other printed materials, DVD-ROMs, website.
You will need
Basic scientific calculator.
Computing requirements
This course includes online computer activities – you can access these using a web browser that can play Flash and Shockwave.
You will need internet access and a computer. If you have purchased a new computer since 2002 it should meet your course computing requirements. Check our Technical Requirements section if your computer is older than this or is otherwise unusual.
Teaching and assessment
Support from your tutor
You will receive support from a team of tutors throughout your study of this course. Members of this team will help you with the course material and comment on your written work, and will be available for you to ask for advice and guidance. There will be a number of etutorials that you can join and access via your computer. You are encouraged, but not obliged, to participate in these. There will also be a number of Day Schools that you are encouraged, but not obliged, to attend. You will also be able to participate in discussions through online forums. Contact our Student Registration & Enquiry Service if you want to know more about study with the OU before you register.
Assessment
The assessment details for this course can be found in the facts box above.
You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.
There will be a mixture of online interactive computer-marked assignments (iCMAs) and short tutor-marked assignments (TMAs), with a total workload equivalent of four full TMAs.
Both the iCMAs and TMAs will focus strongly on learning through practice rather than on assessment. The feedback you receive on your answers will help you to improve your knowledge and understanding of the course material and to develop important skills associated with the course. The feedback on the iCMAs will be instantaneous and hints will be given so that you can refine any incorrect answers. Although your scores on all these assignments will not contribute directly to your course grade, they form an essential part of the learning process and you will be required to submit a proportion of them to complete the course. You will be given detailed information when you start the course.
Professional recognition
This course may help you to gain recognition from a professional body. Download our Recognition leaflets 3.3 Engineering, 3.4 Chartered Institution of Water and Environmental Management, 3.6 Institute of Mathematics and its Applications and 3.8 Scientific Institutions or ask our Student Registration & Enquiry Service for a copy.
Students also studied
Students who studied this course also studied at some time:
Future availability
The details given here are for the course that starts in February 2011. We expect it to be available once a year.
How to register
To register a place on this course return to the top of the page and use the Click to register button. For more information and advice about registration see OU Study Explained.
About this page
An undergraduate course in Mathematics and Statistics and Science.
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This new quantum mechanics course is a twenty-first century version of previous courses offered by the OU (and elsewhere). A ...
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