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 r
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Acknowledgements

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The author of this unit is Peter Sheldon.

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5 The Devonian Period

Before going any further, click on 'View document' below and read pages 76–77 from Douglas Palmer's Atlas of the Prehistoric World. Do not worry too much about all the different names of fish groups in this, the ‘Age of Fishes’.

4.4 Other Wenlock Limestone fossils

Among the other fossils common in the Wenlock Limestone are brachiopods (Figure 12a and b), gastropods (Figure 12c) and bryozoans (Figure 12d). You may need to reread Section 1.3 to remind yourself about various aspects of these groups.

Figure 13 (the unit image) is a reconstruction of a typical scene from a Wenlock Limestone environment. See
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4.1.1 More on trilobites

Many thousands of trilobite species are known, mostly from Cambrian to Silurian rocks, and all were confined to the Palaeozoic Era. By the time trilobites became extinct in the late Permian, their diversity had dwindled to a small number of species, and the group was long past its peak. The variation in trilobite form is enormous, but the basic three-lobed division of the exoskeleton is always present. The number of trunk segments varies from 2 to 40. Not all have eyes. Most are about 2–10
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4.1 Trilobites

As we've seen, the Cambrian explosion left the seas teeming with a huge variety of animals. In the following activity you will study some of the marine life at one particular time in the Palaeozoic Era – the middle part of the Silurian Period, 430 Ma ago. You'll look in detail at some fossils which come from a deposit in the UK called the Wenlock Limestone, famous for its many beautiful fossils. The Wenlock Limestone crops out mainly around Birmingham and the borders of Wales.

Figure
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12 Glossary

You can access the unit glossary by clicking the link below.

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6.1 Introduction

Despite efforts to avoid them, heart disease, heart failure and heart attacks do occur – sometimes with warning symptoms and sometimes without. Cardiologists (doctors specialising in the heart) use a variety of tests to determine the causes of different conditions leading to heart disease. They are then able to guide subsequent treatment. Special tests that are carried out in cardiology departments may include blood pressure measurements, blood tests, electrocardiography, angiography, echoc
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4.6 A balanced diet

Our diet is simply what we eat and drink. Diet does not mean that we are trying to lose weight, although sometimes this is necessary. What we eat is very important, particularly in people with diabetes (as you found out in Section 3). Our wellbeing is influenced by whether or not we eat a balanced diet. A balanced diet is one
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3.2.1 Fats

Fats, also known as lipids, are important components of living tissues, and are used by the body for making cell membranes and for storing energy. Fats come in a variety of different biochemical types, which may be obtained from the diet or can be synthesised within the body. Many cells of the body can convert certain types of fat into others, but by preference, fats will be obtained from the diet, if available. The fatty acids that cannot be synthesised by the body and therefore must
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Acknowledgements

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2.14 Samples and populations

It is no accident that the examples used to illustrate the statistics for repeated measurements of individual quantities were drawn from chemistry and physics. Experiments involving repeated measurements of some quantity are typical of the physical sciences. There are, however, many other types of scientific work in which a typical procedure is to collect data by measuring or counting the members of a sub-set of things which form part of a larger group, and
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2.10.1 Mean and standard deviation for repeated measurements

In everyday terms, everybody is familiar with the word ‘average’, but in science and statistics there are actually several different kinds of average used for different purposes. In the kind of situation exemplified by Table 2, the sort to use is the mean (or more strictly the ‘arithmetic mean’) For a set of measurements, this is de
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2.5 Expressing probability

According to Equation 1, probability is defined as a fraction. However a fraction such as may also be expressed as a decimal number or as a percentage:

 
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1.4 How precise are the measurements?

Scientists are always trying to get better and more reliable data. One way of getting a more precise measurement might be to switch to an instrument with a more finely divided scale. Figure 4 shows parts of two thermometers placed side by side to record the air temperature in a room.

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1.2 Units of measurement

In the UK, two systems of units are in common use. We still use old imperial measures for some things: milk is sold in pints and signposts indicate distances in miles. But for many other everyday measurements metric units have been adopted: we buy petrol in litres and sugar in kilogram bags. A great advantage of metric units is that we no longer have to convert laboriously from imperial units, such as gallons, feet and inches, in order to trade with continental Europe. Also, calculations are
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An introduction to complex numbers
This unit looks at complex numbers. You will learn how they are defined, examine their geometric representation and then move on to looking at the methods for finding the nth roots of complex numbers and the solutions to simple polynominal equations. First published on Mon, 13 Jun 2011 as Author(s): Creator not set

Complex numbers
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.Author(s): Creator not set

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Exploring data: Graphs and numerical summaries
This Unit will introduce you to a number of ways of representing data graphically and of summarising data numerically. You will learn the uses for pie charts, bar charts, histograms and scatterplots. You will also be introduced to various ways of summarising data and methods for assessing location and dispersion.
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Interpreting data: Boxplots and tables
This unit is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. A boxplot is a fairly simple graphic, which displays certain summary statistics of a set of data. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. Boxplots can also be useful for drawing attention to possible outliers in a dat
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