from The Open University
Alternatively you can skip the navigation by pressing 'Enter'.
The Bottom Line: Winter 2015-16: Renewable EnergySaturday, 6th February 2016 17:30 - BBC Radio 4This week The Bottom Line looks at the economics of renewable energy. Read more: The Bottom Line: Winter 2015-16: Renewable Energy
More or Less: E-cigs, politics, school and birthdaysSunday, 7th February 2016 20:00 - BBC Radio 4
Thinking Allowed 2016: Consumerism, Work-life balanceMonday, 8th February 2016 00:15 - BBC Radio 4
Life: BirdsMonday, 8th February 2016 05:00 - Eden Eden
The Bottom Line: Winter 2015-16: Renewable EnergyAvailable for over a yearThis week The Bottom Line looks at the economics of renewable energy. Read more: The Bottom Line: Winter 2015-16: Renewable Energy
Thinking Allowed 2016: Consumerism, Work-life balanceAvailable for over a year
Deplaning: Why is the 747 coming to the end of the runway?For a long time, the 747 has dominated the skies. But Boeing is slowing production. How come? Read more: Deplaning: Why is the 747 coming to the end of the runway?
OpenLearn Live: 5th February 2016A tribute from one poet to another, and a mouse who made a bad choice. Then more free learning... Read more: OpenLearn Live: 5th February 2016
Discovering Wales and Welsh: first stepsThis free course, Discovering Wales and Welsh, introduces you to who the Welsh people are via a... Try: Discovering Wales and Welsh: first steps now
Introduction to bookkeeping and accountingLearn about the essential numerical skills required for accounting and bookkeeping. This free... Try: Introduction to bookkeeping and accounting now
Scattering is fundamental to almost everything we know about the world, such as why the sky is blue. Tunnelling is entirely quantum-mechanical and gives rise to such phenomena as nuclear fusion in stars. Scattering and tunnelling is a free course that investigatyes examples and applications of both these fascinating concepts.
By the end of this free course you should be able to:
- explain the meanings of the emboldened terms and use them appropriately;
- describe the behaviour of wave packets when they encounter potential energy steps, barriers and wells;
- describe how stationary-state solutions of the Schrödinger equation can be used to analyse scattering and tunnelling;
- for a range of simple potential energy functions, obtain the solution of the time-independent Schrödinger equation and use continuity boundary conditions to find reflection and transmission coefficients;
- present information about solutions of the time-independent Schrödinger equation in graphical terms;
- evaluate probability density currents and explain their significance;
- describe and comment on applications of scattering and tunnelling in a range of situations including: three-dimensional scattering, alpha decay, nuclear fusion in stars, and the scanning tunnelling microscope.
- Current section: Introduction
- Learning outcomes
- 1 What are scattering and tunnelling?
- 2 Scattering: a wave-packet approach
- 3 Scattering: a stationary-state approach
- 4 Tunnelling: wave packets and stationary states
- 5 Applications of tunnelling
- 6 Summary
- Keep on learning
Study this free course
Enrol to access the full course, get recognition for the skills you learn, track your progress and on completion gain a statement of participation to demonstrate your learning to others. Make your learning visible!
Scattering and tunnelling
In this unit we shall consider two physical phenomena of fundamental importance: scattering and tunnelling. Each will be treated using both a stationary-state approach and a wave-packet approach.
We can consider two approaches to describing the state of a system in wave mechanics. In cases where the probability distributions are independent of time, a stationary-state approach can be used. In other cases, where probabilities are time-dependent and motion is really taking place, a wave-packet approach can be used. The two approaches are related but different. In many situations the choice of approach is obvious and straightforward, but that is not always the case, as you will soon see.
You will need to be familiar with some mathematical topics to gain the most from this unit. The most important are differential equations, in particular the solution of partial differential equations using the technique of separation of variables, and complex numbers. This material is available in the Mathematics and Statistics topic of OpenLearn, in the units MST209_10 Modelling with Fourier series and M337_1 Introduction to complex numbers.
You may also find it useful to refer to the original glossary and Physics Toolkit as you work through this unit. PDFs of these documents have been attached in the Summary.
This unit is an adapted extract from the Open University course
Copyright & revisions
Originally published: Thursday, 31st March 2011
Last updated on: Tuesday, 19th July 2011
- Creative-Commons: The Open University is proud to release this free course under a Creative Commons licence. However, any third-party materials featured within it are used with permission and are not ours to give away. These materials are not subject to the Creative Commons licence. See terms and conditions. Full details can be found in the Acknowledgements and our FAQs section.
- This site has Copy Reuse Tracking enabled - see our FAQs for more information.
If you enjoyed this, why not follow a feed to find out when we have new things like it? Choose an RSS feed from the list below. (Don't know what to do with RSS feeds?)
Remember, you can also make your own, personal feed by combining tags from around OpenLearn.
All our alternative formats are free for you to download, for more information about the different formats we offer please see our FAQs. The most frequently used are Word (for accessibility), PDF (for print) and ePub and Kindle to download to eReaders*.
*Please note you will need an ePub and Mobi reader for these formats.