What is Quantum Mechanics? A Physics Adventure

584 Pages·1996·31.72 MB·English

by  Transnational College of LEX

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A PHYS ICS ADV ENT URE
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WHAT IS QUANTUM
MECHANICS?
A Physics Adventu re
Written by
Transnational College of LEX
Translated by John Nambu
Language Research Foundation
BOSTON
What is Quantum Mechanics? A Physics Adventure
Published by:
Language Research Foundation, 68 Leonard Street, Suite 301, Belmont, MA 02478-2566 USA
E-mail: [email protected], www.lexlrf.org
First Published 1996. Copyright © 1996 by Transnational College of LEX
Second Printing 1997
Third Printing 2000
Fourth Printing 2002
Fifth Printing 2004
Library of Congress Catalog Card Number: 95-80427
ISBN 0-9643504-1-6
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying, recording, or by any information storage
and retrieval system, without permission in writing from the Publisher. The Publisher has made
every effort to trace the ownership of all copyrighted material and to secure the necessary
permissions. In the event of any question arising as to the use of any material, the Publisher, while
expressing every regret for any inadvertent error, will be happy to make any necessary corrections.
Printed in the United States of America 1098765
Acknowledgments
Writing and producing the original version and the translation of this book has involved many
people. It gives us great pleasure to acknowledge those people who have taken time to help and
advise us with our projects.
Advisors to the English version
Yoichiro Nambu, Ph.D., Elementary Particle Physics at Enrico Fermi Institute, University of
Chicago
Dr. Matthias Nolte, Ph.D., Crystallography, Harvard University
Japanese Language Services, Boston
Advisors to the original Japanese version
Genpei Akasegawa, artist, writer, photographer
Jiro Ohta, Ph.D., Cell Biology, President of Ochanomizu University
Tan Sakakibara, Automatic Control Engineering, Director of LEX Institute
Hiroshi Shimizu, Ph.D., Biological Complexity and Information, The Ba Research Institute,
Kanazawa Institute of Technology & International Media Foundation
Yusuke Tsukahara, Technical Research Institute in Toppan Printing Co.
Yao Nakano, Senior Fellow at the LEX Institute
Tern Hayashi, Ph.D., Control and System Engineering, Professor Emeritus of Tokyo Institute of
Technology / Professor of Toin University of Yokohama
Toyoo Maeda, Ph.D., Metallurgist, IHI Research Institute Vice-Director
Junichi Miida, Ph.D., Nuclear Engineering, Japan Atomic Energy Research Institute (1956-1981),
Deputy Director / Nuclear Science and Engineering, OECD Nuclear Energy Agency,
Paris (1976-1979), Deputy Director
Shigeyuki Minami, Ph.D., Electromagnetism, Osaka City University
Kazuo Yamazaki, Ph.D., Theoretical Physics, Professor Emeritus of Kyoto University / Professor
of Kobegakuin University
Keiko Nakamura, Ph.D., Biohistory, Biohistory Research Hall Deputy Director General/Professor
of Osaka University
Takao Saito, Ph.D., Space Physics, Professor Emeritus of Tohoku University
Hippo Family Club Members who joined in the Quantum Lectures
Cover
Illustration by Karyl Klopp, Boston, MA.
Designed by Rodelinde Albrecht, Lee, MA.
FOREWORD
to the English-Language Edition
What is Quantum Mechanics? A Physics Adventure is the English translation of Adventures in
Quantum Mechanics (original title: .;. ~1Jl!f..0) ~~) which was first published in Japan in 1991.
Like its predecessor, Who is Fourier? A Mathematical Adventure, which is now on sale in the
U.S., it was translated from Japanese. Both books were originally written by students of the
Transnational College of LEX, or TCL. The English editions were a cooperative effort between
the TCL students and the translators in the U.S., and were produced in Japan.
We are very thankful for the continued support we have received since 1991 from the readers
of the original Japanese version of What is Quantum Mechanics? It has sold over 40,000 copies
(as of September 1995) and has become a long running best-seller. The majority of our readers
are in their 20's and 30's, with one quarter of the total consisting of students. In addition, the book
has been well received by many high school teachers and university professors who have utilized
it as supplementary reading for their classes.
In a world where technological advances are happening at a rapid pace, people who have up
until now not had as much as a hint of interest in quantum mechanics are beginning to discover
and study it. One can see this increased interest just by browsing through the natural sciences
section of major bookstores in Japan and counting the number of books related to quantum
mechanics. Being chosen as one of the most sought after books on the subject by readers is an
honor and has provided us with much confidence and support.
The most unique aspect of this book, if it was summed up in a few words, would be the
process by which this book was produced. In most cases, a person well versed in the sciences,
such as a physics or mathematics professor, would be the author. This book, however, was written
by a group of over 30 lively TCL students who took up the challenge to understand quantum
mechanics. In addition, the first drafts of each chapter were written by those who least understood
the subject when the project began. The joy was overwhelming when those who didn't understand
suddenly did after repeated discussions with members in the same group. People who listened to
the explanations of how these students came to understand were literally drawn into the
presentations because of the happy and powerful mood in which they were conveyed. Another
unique feature of this book is that it can be easily understood by any reader. Its step by step
approach starts at the basics and leaves no stone unturned, down to the very last equation.
This book is derived from the discussions of those students. We think that the reason why the
original Japanese version was so well received was because it is easily understood and its
inclusion of the basics lets even the least knowledgeable feel closer to the subject matter. Great
care was taken to be sure that the happiness and power present in the original version was not lost
in the process of translation. Our hope is that this can be conveyed to the readers of the English
edition. At the same time, we also hope that you will enjoy the real experience of learning the
equations.
Lastly, we would especially like to thank Dr. Yoichiro Nambu, Professor Emeritus of the
University of Chicago, who advised us, and his son, John Nambu, who did the translation work,
for their invaluable help in producing the English edition. Many thanks to all the others who took
the time to assist and support us.
Of course, any errors in this work are strictly our responsibility. We hope that this book will
bring forth many new acquaintances.
January 1996
Transnational College of LEX
v
CONTENTS
FOREWORD to the English-Language Edition v
FOREWORD to the Japanese-Language Edition ix
I NTRODUCTION The General Flow 1
CHAPTER 1 Planck and Einstein What is Light? 23
1. 1 Getting Started 24
1.2 The Slit Experiment 30
1. 3 Blackbody Radiation 34
1. 4 Light is a Particle!? 62
1. 5 The Photoelectric Effect 67
1. 6 The Compton Effect 75
1. 7 Cloud Chamber Experiment 84
1.8 So What is Light!? 88
CHAPTER 2 Bohr Early Quantum Theory 95
2. 1 Setting Off on The Adventure 96
2. 2 The Strange Behavior of Atoms 98
2. 3 Bohr Makes His Appearance 111
2. 4 Early Quantum Theory 121
2. 5 Theoretical Inconsistencies and Methods of Solving Them 141
Appendix The Mechanics Used by Bohr 155
CHAPTER 3 Heisenberg The Birth of Quantum Mechanics 169
3. 1 Let's Review 171
3.2 Solving Harmonic Oscillations with Classical Mechanics! 192
3.3 Building Quantum Theory 211
3. 4 The Completion of Matrix Mechanics 242
3.5 A Conversation with Einstein 281
CHAPTER 4 de BrogUe and Schrodinger Wave Mechanics 285
4. 1 Our Adventure So Far 286
4. 2 Electrons are Waves 290
4. 3 Let's Make Wave Mechanics 298
4.4 Let's Ask Mother Nature! 316
4. 4. 1 STEP 1: Free Space 318
4. 4. 2 STEP 2: Inside the Box 336
4.4.3 STEP 3: Hooke Fields 350
4. 4. 4 STEP 4: The Hydrogen Atom 385
4. 5 Complex Electron Waves 390
CHAPTER 5 Schrodinger So Long, Matrix! 419
5. 1 Seeking a Visual Image 420
5.2 Constructing the SchrOdinger Equation! 426
5.3 So Long, Matrix 485
5.4 Schrodinger's Equation in Jeopardy 494
CHAPTER 6 Born and Heisenberg Departure to A New World 509
6. 1 Having it Out 510
6. 2 Born's Probability Interpretation 528
6. 3 The Uncertainty Principle 542
6. 4 Wrapping Up Quantum Mechanics 552
AFTERWORD 557
INDEX 559
FOREWORD
to the Japanese-Language Edition
WHAT IS HIPPO
FAMILY CLUB?
Everyone had already gathered, hoping Hyon would say exactly that.
This is Shibuya, a lively quarter of Tokyo and a
1/
popular haunt for crowds of young people. Moving
past the big department stores and away from the
energetic shopping streets, you find your way to
Shoto, with its array of large private homes. There
is a white, seven-story building at one corner. When
you look up, bright blue and yellow jump out at you
from the signboard on the middle section of the
building. You can be sure that at certain times, the place is aglow with the
kaleidoscopic stir of people turning, twisting, hands and feet going up and
down. Few can pass by without hearing music, laughter and all manner of odd
sounds coming forth.
Every day, this modest-sized building rings with the light steps of casual
young people, smiling mothers with nursing babies, fathers in suit and tie,
rambunctious children, bright-faced office ladies, and shuffling grandmothers
and grandfathers. Not all of these people coming and going are Japanese -
quite a few are from other countries.
This cheerful, unique place is the main headquarters of the Hippo Family
Club, where their motto is "Let's speak in seven languages!"
Do you know about the Hippo Family Club?
FOREWORD to the Japanese-Language Edition IX
1. Our favorite phrase is "Let's speak in
seven languages", but in the last several
years we have added new languages, and
are currently acquiring eleven languages 2. What is "natural learning"?
-Japanese, English, Korean, Spanish, We don't study so much as
French, Chinese, German, Italian, naturally grow fluent in a
Russian, Thai and Malay - the natural language, like a small child
way. does.
3. We play tapes all the
4. We don't do it alone, of
time - at home, inside
course, in isolation. Groups of
the car, on the way to
families gather together at
school or work, wherever
"multilingual parks" called
we happen to be. Like so
"Families" and sing, dance and
much background music,
practice saying the sounds and
we constantly listen to
words heard on the tapes back
cheerful songs and
and forth to each other. We all
conversations in a
have a great deal of fun while
multitude of different
chanting our new languages.
languages and hum these
sounds to ourselves.
5. As the name Family 6. Since we can go abroad to
Club implies, people of all various countries on our
ages join, from babies, homestay exchange programs, or
children and students to host visitors from abroad at our
young, single working homes, we can get to know
adults, fathers, mothers and people and their families from all
grandparents. Anyone can over the world.
participate no matter who
they are.
f.!v-., For details, please call LEX AMERICA,
~ .3 the North American headquarters of HIPPO!
t;:7) e
Tel: [phone] c,aL
x FOREWORD to the Japanese-Language Edition
Serving as the research division of the Hippo Family Club is the Hippo
institute called the Transnational College of LEX (Tokyo, Japan), commonly
known as TCL, for short. It takes up the entire second floor of the white
building. At TCL there are no tests, and no grades or marks given. Classes are
not divided by grade levels, and attendance is not taken. About fifty students
are currently enrolled, from freshmen to experienced research students. They
range from recent high school graduates to elderly grandmothers.
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What do they do at TCL? " . '1@, , !"
"
o " ' $
Studies center on treating language as a natural science.
8
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At first, I had absolutely no idea what it meant to treat
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language as a natural science, either. The word "nature" evokes
•.! :... images like mountains and seas. So I could understand studying
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,\11' Dai,ll the earth and living things in the natural sciences. In physics as
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well, I could understand why things like how the planets rotate are
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questions for natural science, but as to why an apple falls from a tree, or
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why a ping-pong ball bounces or rolls - that was too much. How could
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these possibly be the objects of natural science, much less human
language ... ?
I I
I I
About the third year after I entered TCL, I finally grasped what it
I I
meant to treat language as a natural science. That's because I discovered
I
that language shares a trait found in other objects of natural science. That
I
common trait is "repetition." To find a language by which we can explain
I
things that occur repeatedly is the basis for natural science.
I
An apple falls from a tree. This happens I
repeatedly, every time an apple grows bigger and
I
its stem weakens. No matter what sort of apple it
I
may be, if the conditions are the same, an apple
I
should fall in just exactly the same way. It never
happens that one apple falls to the ground, while I
another apple climbs up the tree. In the language of physics, which uses I
equations rather than words, this predictable, regular occurrence is
I
described by F = rna.
I
Discovering these regularities is natural science. Human language I
also is a phenomenon of natural science. A baby born in Japan is i
FOREWORD to the Japanese-Language Edition Xl