Interactive quantum mechanics. With CD-ROM.

*(English)*Zbl 1038.81002
New York, NY: Springer (ISBN 0-387-00231-6/hbk). xiii, 306 p. (2003).

This book is an improved and generalized version of the previous and well succeeded “The Picture Book of Quantum Mechanics” by S. Brandt and H. D. Dahmen (Springer, New York) (2001; Zbl 1038.81001). It is probably the most attractive, updated, and easy-to-follow method for learning basic quantum mechanics (QM) in all literature. The reader has so many tools at his/her hands, that I cannot imagine a better way to learn this important but abstract field of modern physics.

First, in 300 pages the authors discuss only very basic issues, namely, free particle systems, bound states, and scattering in one and in three dimensions, two-particle systems, coupled harmonic oscillators, distinguishable and indistinguishable particles, coherent and squeezed states in time-dependent motion, quantized angular momentum, and special functions of mathematical physics. This soft introduction to QM is very important for most students. It provides a solid preparation for advanced studies to be carried on in later courses.

Second, the book presents over 300 class-tested exercises with hints for solutions and 90 figures.

Third, the reader has the opportunity to use a computer laboratory in quantum mechanics by performing computer experiments in a self-explanatory environment provided by the Java programming language that is not more difficult to use than surfing the Internet. Such a virtual laboratory is provided by an included CD-ROM containing the program package INTERQUANTA (the interactive program of quantum mechanics), version 3.0, which is compatible with personal computers running under Windows 95 and upwards (Windows 98, NT 4.0, 2000, ME, and XP), and Linux, Kernell 2.2.xx and upwards. It is also compatible with Macintosh computers running under Mac OS X, Sun Sparc computers under Solaris SunOS 5.8 or higher, IBM Risc Computers under AIX version 4.3.3 or higher, and PowerPC computers under Linux (although this last option is still untested).

Fourth, if the reader does not feel comfortable with reading documents on a computer screen in order to follow some short explanatory texts about quantum mechanical problems that are solved and graphically represented, there is the option of listening to these explanations, if loudspeakers are available at the computer.

Fifth, the minimum hardware requirements are very accessible for almost all practical purposes: processor speed of 200 MHz, RAM memory of 64 MB (except for SunOS and AIX, which demand 128 MB of virtual memory), and 250 MB of disk space.

Neither the book nor the CD-ROM are adequate for understanding some of the major issues of either the foundations or the philosophical/historical developments of quantum mechanics. Instead, this work is quite appropriate for the future working physicist who is interested in the basic mathematical and computational tools and issues of QM and their physical interpretation. But the authors correctly recommend some further reading of some classic textbooks like the Feynman Lectures on Physics, A. Messiah’s, L. I. Schiff’s, and S. Gasiorowicz’s books on QM, and M. Abramowitz and I. A. Stegun’s Handbook of Mathematical Functions, among other references. The cited literature is not large (mainly focused on a few books and one paper), but it is very helpful. In this sense, this book should be understood as a very useful (almost indispensable) support in standard courses on QM.

Nevertheless, sometimes the authors make brief but very interesting foundational discussions in the text. In 1998, e.g., the authors published (with E. Gjonai and T. Stroh) a paper (which is cited and used in the book) where they introduce the concepts of quantile position, quantile velocity, and quantile trajectory [see Phys. Lett. A 249, 265–270 (1998)]. Such quantiles are associated with probability densities and they have a straight relationship with Bohmian mechanics in the sense that Bohm’s particle trajectories are identical to quantile trajectories. Nevertheless, this quantile formalism has the advantage to be defined within the conventional framework of quantum mechanics, where particles cannot have their positions and velocities well known at the same time due to the uncertainty principle. This quantile formalism is sometimes used across the text and across the software.

On the other hand, eventually the reader may feel frustrated at some points of the book. For example, when the authors introduce the Coulomb potential energy in the Hydrogen atom in units \(\hbar c\) (where \(\hbar\) is the reduced Planck’s constant and \(c\) is velocity of light in vacuum) they do not discuss in further details the role of Sommerfeld’s fine-structure constant in QM. Such a constant appears only on pages 134 and 135 in a very ad hoc way, mainly based on a simple change of units.

The reviewer believes that this kind of situation deserves to be revised in future editions of this excellent book. Actually, this kind of situation just demands some minor corrections (for the sake of a self-contained and self-consistent text) in a book that certainly will influence the learning of many students all around the world in a very constructive manner.

First, in 300 pages the authors discuss only very basic issues, namely, free particle systems, bound states, and scattering in one and in three dimensions, two-particle systems, coupled harmonic oscillators, distinguishable and indistinguishable particles, coherent and squeezed states in time-dependent motion, quantized angular momentum, and special functions of mathematical physics. This soft introduction to QM is very important for most students. It provides a solid preparation for advanced studies to be carried on in later courses.

Second, the book presents over 300 class-tested exercises with hints for solutions and 90 figures.

Third, the reader has the opportunity to use a computer laboratory in quantum mechanics by performing computer experiments in a self-explanatory environment provided by the Java programming language that is not more difficult to use than surfing the Internet. Such a virtual laboratory is provided by an included CD-ROM containing the program package INTERQUANTA (the interactive program of quantum mechanics), version 3.0, which is compatible with personal computers running under Windows 95 and upwards (Windows 98, NT 4.0, 2000, ME, and XP), and Linux, Kernell 2.2.xx and upwards. It is also compatible with Macintosh computers running under Mac OS X, Sun Sparc computers under Solaris SunOS 5.8 or higher, IBM Risc Computers under AIX version 4.3.3 or higher, and PowerPC computers under Linux (although this last option is still untested).

Fourth, if the reader does not feel comfortable with reading documents on a computer screen in order to follow some short explanatory texts about quantum mechanical problems that are solved and graphically represented, there is the option of listening to these explanations, if loudspeakers are available at the computer.

Fifth, the minimum hardware requirements are very accessible for almost all practical purposes: processor speed of 200 MHz, RAM memory of 64 MB (except for SunOS and AIX, which demand 128 MB of virtual memory), and 250 MB of disk space.

Neither the book nor the CD-ROM are adequate for understanding some of the major issues of either the foundations or the philosophical/historical developments of quantum mechanics. Instead, this work is quite appropriate for the future working physicist who is interested in the basic mathematical and computational tools and issues of QM and their physical interpretation. But the authors correctly recommend some further reading of some classic textbooks like the Feynman Lectures on Physics, A. Messiah’s, L. I. Schiff’s, and S. Gasiorowicz’s books on QM, and M. Abramowitz and I. A. Stegun’s Handbook of Mathematical Functions, among other references. The cited literature is not large (mainly focused on a few books and one paper), but it is very helpful. In this sense, this book should be understood as a very useful (almost indispensable) support in standard courses on QM.

Nevertheless, sometimes the authors make brief but very interesting foundational discussions in the text. In 1998, e.g., the authors published (with E. Gjonai and T. Stroh) a paper (which is cited and used in the book) where they introduce the concepts of quantile position, quantile velocity, and quantile trajectory [see Phys. Lett. A 249, 265–270 (1998)]. Such quantiles are associated with probability densities and they have a straight relationship with Bohmian mechanics in the sense that Bohm’s particle trajectories are identical to quantile trajectories. Nevertheless, this quantile formalism has the advantage to be defined within the conventional framework of quantum mechanics, where particles cannot have their positions and velocities well known at the same time due to the uncertainty principle. This quantile formalism is sometimes used across the text and across the software.

On the other hand, eventually the reader may feel frustrated at some points of the book. For example, when the authors introduce the Coulomb potential energy in the Hydrogen atom in units \(\hbar c\) (where \(\hbar\) is the reduced Planck’s constant and \(c\) is velocity of light in vacuum) they do not discuss in further details the role of Sommerfeld’s fine-structure constant in QM. Such a constant appears only on pages 134 and 135 in a very ad hoc way, mainly based on a simple change of units.

The reviewer believes that this kind of situation deserves to be revised in future editions of this excellent book. Actually, this kind of situation just demands some minor corrections (for the sake of a self-contained and self-consistent text) in a book that certainly will influence the learning of many students all around the world in a very constructive manner.

Reviewer: Adonai S. Sant’Anna (Curitiba)

##### MSC:

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

81Qxx | General mathematical topics and methods in quantum theory |

81Rxx | Groups and algebras in quantum theory |

81Sxx | General quantum mechanics and problems of quantization |

81-08 | Computational methods for problems pertaining to quantum theory |