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Schrödinger’s Mechanics Interpretation Q0143hc_9781786344908_TP.indd 1 5/3/18 8:41 AM Other World Scientific Titles by the Author Schrödinger’s Mechanics ISBN: 978-9971-5-0760-2 Probability and Schrödinger’s Mechanics ISBN: 978-981-238-191-0 Quantum Chemistry: A Unified Approach Second Edition ISBN: 978-1-84816-746-9 Herbert Moses - Q0143 - Schrödinger's Mechanics.indd 1 06-03-18 3:28:56 PM Schrödinger’s Mechanics Interpretation David B Cook University of Sheffield, UK World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO Q0143hc_9781786344908_TP.indd 2 5/3/18 8:41 AM Published by World Scientific Publishing Europe Ltd. 57 Shelton Street, Covent Garden, London WC2H 9HE Head office: 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 Library of Congress Cataloging-in-Publication Data Names: Cook, David B. (David Branston), author. Title: Schrödinger’s mechanics : interpretation / by David B. Cook (University of Sheffield, UK). Description: New Jersey : World Scientific, 2018. Identifiers: LCCN 2017052617 | ISBN 9781786344908 (hc : alk. paper) Subjects: LCSH: Wave mechanics. | Schrödinger equation. | Schrödinger operator. | Quantum theory. | Numerical analysis. Classification: LCC QC174.26.W28 C6574 2018 | DDC 530.12/4--dc23 LC record available at https://lccn.loc.gov/2017052617 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2018 by World Scientific Publishing Europe Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. For any available supplementary material, please visit http://www.worldscientific.com/worldscibooks/10.1142/Q0143#t=suppl Desk Editors: Herbert Moses/Jennifer Brough/Koe Shi Ying Typeset by Stallion Press Email: [email protected] Printed in Singapore Herbert Moses - Q0143 - Schrödinger's Mechanics.indd 2 06-03-18 3:28:56 PM March7,2018 5:9 Schrödinger’sMechanics:Interpretation-9inx6in b3108-fm pagev Preface There is no shortage of books about the interpretation of quantum theories; they range from the ‘what do I need to know’ type to fantastic and unverifiable conjectures about the nature of the universe(s), why should one get involved in such a knotty area of dispute? What I would like to do in this short account is to emphasise that the original form of Quantum Mechanics is not a series of useful formulae for interpreting experimental results nor does itrequireany newphilosophies,itis acogent interpreted theory of the behaviour of sub-atomic particles and has been as successful in this region as Newtons mechanics has been in the familiar world. In this context we academics all write, in our ‘Mission Statements’ and our ‘Self-evaluations of Teaching’, that we encourage, even insist on, a critical, scientific attitude to learning. But where is this critical attitude encouraged and what type of criticism is to be elicited from our students? Of course, we encourage a critical attitude to the quality and reliability of experimental data — error analysis and all that — but this is just routine, little more than a formalisation of common sense and good housekeeping. Only very rarely is a criticism of the theories of science and their interpretation encouraged and if it is, this criticism is to be found in formal courses in ‘History and Philosophy of Science’ and not in the real everyday process of confronting current science in our teaching and research. One is reminded of the saying “every generation must write history anew v March7,2018 5:9 Schrödinger’sMechanics:Interpretation-9inx6in b3108-fm pagevi vi Schro¨dinger’s Mechanics: Interpretation for itself”; much lip service and very little practice. In fact, if every generation of scientists does not rework the theories which they have been taught ‘for themselves’ (at least in outline) then science stagnates and becomes a set of recipes; just another set of axioms to be manipulated. This work is the outcome of many years — mostly post- retirement — of musing about quantum mechanics and its interpretation. In this, I have been mainly influenced by what I have called elsewhere Schrödinger’s Mechanics (henceforth SM); the mechanics developed by Schro¨dinger in his astonishing paper of 1926. During these years I have come to realise more and more the absolutely central importance of the method developed in this paper. I shall want to say more about the strange fact that this paper is now largely unread and the methods used in it apparently unknown. So, this work could be described as ‘old hat’ in that it is almost a century since this pioneering publication; but the disagreements about the interpretation of SM and all of the quantum mechanics which followed is certainly not so antique, indeed it is an open sore in physics. In previous publications I have concentrated on the non- relativistic SM while occasionally promising to have a more careful look at the problem of making quantum mechanics compatible with Special Relativity, that is to see how to introduce Lorentz invariance onto the scene. Special Relativity has played hardly any part in my professional research (quantum chemistry) and I have always had a strong suspicion that the idea that electron ‘spin’ somehow depends onSpecialRelativityissuspect.Thisisnaturallyduetomyprejudice, as a chemist, against Dirac’s physical interpretation of his ‘pretty a mathematics’ when applied to another phenomenon — the theory of the chemical bond as ‘spin coupling’ — which was a red herring in the physical interpretation of the driving force of bond formation for decades. I have addressed the matter of spin in Chapter 6. In this work I will show that, when equipped with a realistic interpretation, the methods of Schro¨dinger’s 1926 paper contain aInternational Journal of Theoretical Physics, 21(8–9), pp. 603–605. March7,2018 5:9 Schrödinger’sMechanics:Interpretation-9inx6in b3108-fm pagevii Preface vii either explicitly or implicitly all other formulations of Quantum Mechanics. And I use ‘contain’ deliberately; SM is not ‘equivalent to’ other formulations, it includes them in the sense that many ‘principles’ (axioms) of other methods are theorems in SM. What is true, however, is that SM shares some formal (mathematical) structures with other theories; but that is extremely common in mathematically articulated sciences; all that this means is that certain formal mathematical structures may be abstracted from SM. What makes SM unique is its physical interpretation and its explicit and transparent links to Classical Particle Mechanics. With the historicaldevelopmentofmethodsallegedly basedonorderivedfrom SM has come a retreat from physical interpretation in general and the very idea of submittingone’s theories to independentverification is often abandoned. In criticising the standard interpretations of quantum theories I am very aware of the possible shortcomings of such work as aptly described by Kenneth Tynan’s ‘definition’: “A critic is a man [sic] who knows the way but can’t drive the car”. Awordor two aboutmy eccentricities: Iusethewordabstract as both an adjective and, more often, as a verb. Also, I have purposely tended to refer to older publications since these earlier authors were struggling to understand the meaning of all the new theories in science not simply to work from what are regarded as standard interpretations. I have used appendices and endnotes as well as the occasional footnote; footnotes are indicated by the traditional symbols (∗, † etc.) and the endnotes, which tend to be longer, by numbers. I hope that the book could be read simply by reading the chapters leaving appendices and endnotes for some clarification. Some principle points are repeated or referred to from time-to-time for the reader who, like myself, tends to dip into a book without reading from the start! I am thinking of this essay as some form of reculer pour mieux sauter. I can try the reculer part and I leave the mieux sauter to others. David B. Cook b2530 International Strategic Relations and China’s National Security: World at the Crossroads TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk b2530_FM.indd 6 01-Sep-16 11:03:06 AM March7,2018 5:9 Schrödinger’sMechanics:Interpretation-9inx6in b3108-fm pageix About the Author Dr. David B. Cook is an Associate of the University of Sheffield, England. He graduated from the University of Sheffield with a B.Sc. in 1962, postgraduation (PhD) in 1966, and a D.Sc. in 1989. He served as a Postdoctoral Fellow along with Prof. Roy McWeeny at Keele University, England, in the year 1966. During his tenure from 1967 to 2003 at the University of Sheffield, he has been a Lecturer, a Senior Lecturer, and a Director of Studies. His earlier published books include Ab Initio Valence Calculations in Chemistry (Butterworths, 1974), Structures and Approximations for Electrons inMolecules (EllisHorwood,1978),Schrödinger’s Mechan- ics (World Scientific, 1988), Handbook of Computational Quantum Chemistry (OUP, 1998), Probability and Schro¨dinger’s Mechanics (ImperialCollegePress,2002),Handbook of Computational Quantum Chemistry (Revised Edition) (Dover Publications, 2005), Quantum Chemistry: A Unified Approach (Imperial College Press, 2008), and Quantum Chemistry: A Unified Approach (Revised Second Edition) (Imperial College Press, 2012). He has published over 60 scientific papers in the areas of the theory and implementation of the calculation of molecular electronic structure; in three-quarters of these, he was the sole author. ix