by Siegmund Brandt, Hans Dieter Dahmen and Tilo Stroh, Springer-Verlag. Hardback ISBN 387002316, €69.95 (£54.00, $69.95).
“Physical intuition” is a precious commodity for all physicists. Richard Feynman, when asked once what his intuition was concerning a certain problem, is said to have replied that he didn’t have any because he hadn’t done the calculation yet. Common sense is frequently a poor guide, even in the classical domain, but there our intuition can be built up with the help of reasoned interpretations of phenomena we can experience directly, and by the performance of many relatively simple and realistic calculations. Gaining intuition about the quantum world is much harder: we have little, if any, direct perception of it, and few realistic problems are mathematically easy to solve. Thus, students have a hard time “thinking physically” when faced with quantum problems.
Surely computers ought to be able to help. Quite complicated problems can be quickly solved numerically, and – most importantly – the results can be presented in a variety of graphical forms. Indeed, several recent undergraduate texts on quantum mechanics have included disks demonstrating the solutions of standard problems. These generally have a modest capability for the student to “play with the parameters”, but there has been nothing more radically interactive. This book is the first (so far as I know) to fill this gap.
In fact, it might be more accurate to describe it as a computer program on a CD, accompanied by extended notes, rather than as a book accompanied by a CD. The program, called “INTERQUANTA” or IQ for short, has a self-explanatory user interface written in Java. It is easy to install and simple to work with – the instructions are even suitable for computer illiterates like myself. It can be used passively, to watch (and listen to) demonstrations that illustrate the main points in the text, but in the second, interactive mode the user is offered considerable freedom in designing the problems to be solved and the ways in which the answers may be displayed. As the authors put it, users can enter a “computer laboratory in quantum mechanics”.
Eight physics topics are treated in as many chapters: free-particle motion, bound states and scattering, first in one and then in three dimensions; two-particle systems in one dimension; and special functions of mathematical physics. Each chapter begins with a section called “Physical Concepts”, in which the relevant concepts and formulae are assembled without proof. Each section of the text is carefully keyed to a corresponding part of IQ, and the graphical outputs are well designed and easy to read. More than 300 numerical exercises are included to stimulate the reader’s exploration, and many contain useful prompts encouraging the reader to suggest a physical explanation for particular results. A final chapter contains hints for the solution of some exercises, and an appendix provides a systematic guide to IQ.
IQ contains much useful material, and the authors are to be congratulated on having produced something rather novel that is so user friendly. But I believe its value would be greatly enhanced if the range of topics were to be significantly extended. For example, all the presentations are static, yet there are many fascinating and important time-dependent phenomena in quantum theory for which a “movie” would be a valuable aid to understanding. And it is a pity that the whole vital area of perturbation theory is omitted, where there is ample scope for numerical instruction. A program that included topics such as these would surely be a major resource for both students and teachers.
