The Basic Physics Of Quantum Theory

207 Pages·2020·16.518 MB·English

by  Davis Basil S

The Basic Physics of
Quantum
Theory
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The Basic Physics of
Quantum
Theory
Basil S Davis
Xavier University of Louisiana, USA
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
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Published by
World Scientific Publishing Co. Pte. Ltd.
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Library of Congress Control Number: 2020015390
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
THE BASIC PHYSICS OF QUANTUM THEORY
Copyright © 2020 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 978-981-121-939-9 (hardcover)
ISBN 978-981-121-995-5 (paperback)
ISBN 978-981-121-940-5 (ebook for institutions)
ISBN 978-981-121-941-2 (ebook for individuals)
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/11801#t=suppl
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Preface
This book arose out of a one-semester class for non-science majors that I
taught at Tulane University in Fall 2016. None of the students had taken
any college level physics, and some had studied no physics even in high
school. While it is fair to say that the course challenged the students, all
33ofthempassedtheclass, therebydemonstratingtheiradequategraspof
quantum theory. I therefore know from experience that anyone can learn
quantumtheorywiththeproperguidance. AndsoIhavewrittenthisbook
forallwhowishtolearnthissubject,tobeusedeitherasacollegetextbook
or by individual readers who wish to improve their own understanding of
physics.
I owe a special debt of gratitude to Dr. Jim McGuire, who as Chair of
the physics department of Tulane invited me to do a doctorate in physics,
to Dr. Lev Kaplan, my doctoral advisor, whose cheerful patience made
every one of our meetings a delight, and to Dr. John Perdew, who as my
quantum mechanics professor inspired a deep love for the subject in me.
It is seldom that one meets such brilliant physicists who are also men of
genuine compassion with a total commitment to their students. It is a
matter of pride and honor for me to call them my friends.
IamparticularlygratefultomywifeShylawhogaveherfullsupportto
my decision to pursue a career in science and embraced the challenges that
accompanied that decision. It is with much love that I dedicate this book
to Shyla and to our three children Melinda, Jessica and Peter who have
accompanied me, whether they like it or not, in my quest for the ultimate
realities of the universe.
Basil S. Davis
New Orleans, 2020.
v
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Contents
Preface v
1. Introduction 1
1.1 A new understanding of reality . . . . . . . . . . . . . . . 1
1.2 A theory of particles and fields . . . . . . . . . . . . . . . 2
1.3 Outline of the book . . . . . . . . . . . . . . . . . . . . . . 5
2. Newtonian Physics 7
2.1 Observation of the night sky . . . . . . . . . . . . . . . . . 7
2.2 Measurement of time . . . . . . . . . . . . . . . . . . . . . 8
2.3 Ptolemy’s model . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 The Copernican revolution . . . . . . . . . . . . . . . . . . 10
2.5 Newton’s laws . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Work and energy . . . . . . . . . . . . . . . . . . . . . . . 16
2.7 Determinism. . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3. Statistical Mechanics 21
3.1 Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 The laws of thermodynamics . . . . . . . . . . . . . . . . 22
3.3 Statistical mechanics . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 One-dimensional gas . . . . . . . . . . . . . . . . . 27
3.3.2 Two-dimensional gas . . . . . . . . . . . . . . . . 29
3.3.3 Three-dimensional gas . . . . . . . . . . . . . . . . 30
3.3.4 Third law of thermodynamics . . . . . . . . . . . 30
3.3.5 Second law of thermodynamics . . . . . . . . . . . 31
vii
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viii The Basic Physics of Quantum Theory
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4. The Concept of a Field 35
4.1 Action at a distance . . . . . . . . . . . . . . . . . . . . . 35
4.2 Electricity and magnetism . . . . . . . . . . . . . . . . . . 36
4.3 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Electromagnetic waves . . . . . . . . . . . . . . . . . . . . 42
4.5 Finite speed of fields . . . . . . . . . . . . . . . . . . . . . 44
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5. The Ultraviolet Catastrophe 47
5.1 A black body . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Black body cavity. . . . . . . . . . . . . . . . . . . . . . . 48
5.3 Standing waves and the catastrophe . . . . . . . . . . . . 49
5.4 Escape from the ultraviolet catastrophe . . . . . . . . . . 51
5.5 A small beginning . . . . . . . . . . . . . . . . . . . . . . 53
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6. Absorption and Emission of Radiation 55
6.1 Photelectric effect . . . . . . . . . . . . . . . . . . . . . . . 55
6.2 Einstein’s explanation . . . . . . . . . . . . . . . . . . . . 57
6.3 Momentum of electromagnetic radiation . . . . . . . . . . 58
6.4 Compton effect . . . . . . . . . . . . . . . . . . . . . . . . 59
6.5 Finite time of interaction. . . . . . . . . . . . . . . . . . . 61
6.6 Uncertainty principle . . . . . . . . . . . . . . . . . . . . . 62
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7. Matter Waves 69
7.1 De Broglie’s hypothesis. . . . . . . . . . . . . . . . . . . . 69
7.2 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.2.1 Combination of waves . . . . . . . . . . . . . . . . 70
7.3 Waves in two or three dimensions . . . . . . . . . . . . . . 72
7.4 Quantum theory of light . . . . . . . . . . . . . . . . . . . 75
7.5 Electron waves . . . . . . . . . . . . . . . . . . . . . . . . 78
7.6 Composite particles . . . . . . . . . . . . . . . . . . . . . . 78
7.7 The hydrogen atom . . . . . . . . . . . . . . . . . . . . . . 79
7.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
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Contents ix
8. The Special Theory of Relativity 85
8.1 Speed of light . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.2 Relative speed in classical mechanics . . . . . . . . . . . . 85
8.3 Motion relative to source of light . . . . . . . . . . . . . . 86
8.4 Principles of special relativity . . . . . . . . . . . . . . . . 87
8.5 Relative speed according to Einstein . . . . . . . . . . . . 88
8.6 Impossible to attain the speed of light . . . . . . . . . . . 89
8.7 Length is relative . . . . . . . . . . . . . . . . . . . . . . . 90
8.8 Time ordering of events is relative . . . . . . . . . . . . . 92
8.9 Duration of time is relative — time dilation . . . . . . . . 93
8.10 Mass increases with speed . . . . . . . . . . . . . . . . . . 94
8.11 Mass and energy . . . . . . . . . . . . . . . . . . . . . . . 95
8.12 Relativity and quantum theory . . . . . . . . . . . . . . . 96
8.13 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9. The Geometry of Space and Time 99
9.1 Space time . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9.1.1 World lines . . . . . . . . . . . . . . . . . . . . . . 99
9.1.2 Space-like, time-like and light-like intervals . . . . 100
9.1.3 Minkowski space . . . . . . . . . . . . . . . . . . . 102
9.2 Feynman diagrams . . . . . . . . . . . . . . . . . . . . . . 102
9.3 Arrow of time . . . . . . . . . . . . . . . . . . . . . . . . . 104
9.3.1 Time reversal and Feynman diagrams . . . . . . . 105
9.3.2 Information carried by many photons . . . . . . . 109
9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
10. The Heart of Quantum Theory 113
10.1 How does one study the quantum? . . . . . . . . . . . . . 113
10.2 Fields and states . . . . . . . . . . . . . . . . . . . . . . . 116
10.3 Complex numbers in quantum mechanics. . . . . . . . . . 117
10.4 States and operators . . . . . . . . . . . . . . . . . . . . . 118
10.5 Physical meaning of symbols. . . . . . . . . . . . . . . . . 119
10.5.1 Creation and annihilation of photons . . . . . . . 119
10.5.2 Propagation of a photon . . . . . . . . . . . . . . 121
10.5.3 Probability amplitudes . . . . . . . . . . . . . . . 122
10.5.4 Addition of paths . . . . . . . . . . . . . . . . . . 123
10.6 Classical and quantum probabilities. . . . . . . . . . . . . 123
10.6.1 Constructive and destructive interference . . . . . 124