The quantum world
If you're interested in the fundamental laws of modern physics and how mathematics is used to state and apply these laws, this module 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 module also presents recent evidence relating to some of the most surprising and non-classical predictions of quantum mechanics.
What you will study
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 module 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 study 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 wave packet is introduced and used to describe the classical limit of quantum mechanics. Finally, the quantum processes of tunnelling, barrier penetration and reflection are discussed, together with their application to nuclear fusion, alpha decay, and the scanning tunnelling 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 module, 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.
This module, when studied as part of an honours degree in the physical sciences or engineering, can help you gain membership of the Institute of Physics (IOP). For further information about the IOP, visit their website.
This module may also help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.
This is an OU level 3 module that builds on study skills and subject knowledge acquired from previous studies at OU levels 1 and 2. It is intended for students who have recent experience of higher education in a related subject at this level.
The module is designed to follow Mathematical methods (MST224) (or Mathematical methods, models and modelling (MST210) and Physics: from classical to quantum (S217) ( or The physical world (S207) now discontinued). You would find it very difficult to study SM358 without the necessary mathematical background. The parts of MST224 or MST210 relating to matrices, ordinary and partial differential equations are especially important. Either S207 or S217 is the ideal physics module to prepare you for studying SM358, particularly the parts relating to classical and quantum mechanics. Students are most successful if they have acquired their prerequisite knowledge through passing these two OU level 2 modules.
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? The quantum world to help you decide whether you already have the recommended background knowledge and experience to start the module or whether you need some extra preparation.
If you have any doubt about the suitability of the module, please speak to an adviser.
Module books, other printed materials, DVD-ROMs, website.
You will need
Basic scientific calculator.
A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.
Any additional software will be provided from a hardware device e.g. DVD drive or USB stick or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a desktop or laptop computer with Windows 7 or higher.
The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.
To participate in our online-discussion area you will need both a microphone and speakers/headphones.
Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.