Scattering and tunnelling

Introduction

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 The quantum world (SM358) [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]