Table of contents

Johann Bernoulli's brachistochrone problem is now three hundred years old. Bernoulli's solution to the problem he had proposed used the optical analogy of Fermat's least-time principle. In this analogy a light ray travels between two points in a vertical plane in a medium of continuously varying index of refraction. This solution and connected material are explored in this paper.

A new solution of Rayleigh's equations for a loaded flexible string is presented. The particular case of a midpoint mass is discussed in detail. A possible application to a struck string is developed and compared with experimental data.

The exact equation of motion for a plucked flexible string is compared at second-order level with the D'Alembert approximation. Important differences are demonstrated and discussed. A simplifying hypothesis is proposed.

A measurement of the altitude of the Teide peak on Tenerife in the Canary Islands calculated by Spanish and French naval officers from barometric and thermometric data in 1776 is presented here. The observations are described and the result obtained is discussed.

In each of the inertial reference frames in relative motion, a clock synchronization procedure is performed by a light signal emitted by a source at rest in the corresponding frame and located at its origin. The fact that the velocities at which the light signals propagate are equal to each other obscures the part played by each of them in an equation which describes a relativistic effect. Supposing that the two velocities are different (c in the stationary frame, c´ in the moving one), the positions of c and c´ in a relativistic formula are specified.

Making astronomy more accessible and attractive to students is very important. In keeping with this objective, we present an activity on teaching planetary motion and the relative positions of the Sun, Earth and an inner or outer planet. We give special consideration to the phases of an inner planet and the gibbous appearance of an outer planet to motivate the interest of the students.

This paper presents a simple study of the relative position and the phases of the planets. The contents are appropriate for university students, although not only for astronomy degree students. This presentation is suitable for students of other degrees, who are studying a basic course in astronomy. This activity could follow the general study of Kepler's laws and elliptic motion. Its aim is to explain observations using the general theory of elliptic motion, so that students can understand this theory in greater depth. They study an especially interesting phenomenon, despite not being very well known by ordinary people, which is the different appearance of the planets depending on whether they are inner or outer planets.

A group of evocative images of Venus and Mars are used to introduce the study of elliptic motion. We take care to present the results obtained using simple and schematic diagrams to facilitate its understanding. Finally, we present a simple mathematical model for carrying out the calculations related to angles and relative distances and we compare the results obtained by this simplified process with the parameters obtained directly from the photographs, and with the values calculated by elliptic motion.

Due to the difficulties encountered in several aspects of experimental error estimation, undergraduate physics students usually use a list of `recipes' instead of taking a specific experimental errors course. Consequently, it is common to find university students who confuse basic concepts in the adjustment of experimental data. In this paper, the most conflicting points concerning linear regression are briefly reviewed. Confidence bands and a discussion about the use of a line through the origin are also included. In addition, the simplest expressions for expressing parameters to the appropriate significant figures from built-in calculator programs are also provided.

I criticize the claim, made in a recent article (Bender C M and Mead L R 1999 Eur. J. Phys. 20 117-21) that, in order to obtain the correct cross section for the scattering from a two-dimensional delta-function potential, one must perform analytic continuation in the dimension of space.

This note offers two comments on a recent paper in this journal (Antippa A F 1998 Eur. J. Phys.19 413-7).

In a recent paper (Avron J E, Berg E, Goldsmith D and Gordon A 1999 Eur. J. Phys.20 153-9) a paradox in which the number of photons seemed to depend on the reference frame was presented. Another resolution of this paradox can be found in the 1905 relativity paper of Einstein.

Dimensional analysis of the formula for the fine-structure constant does not provide evidence that one of the constants c, , or e is not fundamental. Natural systems of units based on the velocity of light c, Planck's constant , and the electric charge e are possible and prospective for quantum metrology. In these systems, the coefficient in the Coulomb law is numerically equal to the fine-structure constant 1/137.

The dissipation of a highly localized harmonic oscillator wave packet of Gaussian form and its subsequent revival (and the revival of wave packets in an infinite square well) are discussed; these examples are evocative of the echoes encountered in many domains of physics.

After a short review of some essential concepts of classical physics (with a discussion of the so-called `scientific method', which is rarely found in textbooks of this kind), including the classical description of particles and waves, together with a sketch of statistical thermodynamics, the basics of quantum mechanics are introduced. The third chapter then treats systems of identical particles and their statistics, as well as the statistics of discrete energy levels. This is followed by an extensive presentation of the behaviour of quantum particles in periodic potentials with obvious applications to crystalline materials, including metals, insulators, semiconductors and superconductors. The band structure of some special materials, intrinsic carrier concentrations and electrons in metals are further topics of this main chapter. In most quantum mechanics textbooks the subjects of the fifth chapter, quantum wells, harmonic oscillators and the hydrogen atom, are usually introduced before a discussion of periodic potentials, but the author's exposition makes it quite plausible to place them afterwards. The concept of tunnelling through potential barriers and important application examples, ranging from ohmic contacts to scanning tunnelling microscopy and even radioactivity, make up the next chapter. Some approximation methods, i.e. stationary perturbation theory with applications to coupled wells, and the variational method, are treated in the next chapter. The final chapter dealing with quantum mechanics then is concerned with scattering and collision problems, again, of course, with examples from solid state physics. This last chapter, however, looks somehow merely added on, since it introduces only quite briefly the theory of special relativity -almost certainly in order not to leave out this important revolution of modern physics. Three appendices, on Fermi's Golden Rule, Boltzmann's transport theory and quantum interference devices, round off the contents. The book abounds with links to modern technologies that have evolved out of quantum mechanics (with, of course, the exception of the last chapter on special relativity). To the reviewer this constitutes its outstanding value as a textbook on quantum mechanics for engineering students. In addition, about 100 solved numerical examples in the text illustrate very lucidly some of the more abstract concepts, and at the end of the chapters altogether 200 further problems are posed. Although some of the concepts and results of quantum mechanics are introduced in a seemingly ad hoc manner, nevertheless the book as a whole certainly represents a valuable teaching tool at engineering schools; even physics majors may profit from the wealth of technical applications not usually found in their textbooks on quantum mechanics.

The substantive part of the book is devoted to elementary quantum mechanics (Chapters 1-3) and some elements of statistical mechanics (Chapters 5-6), starting with basic concepts in quantum mechanics, which, as mentioned earlier, could really be skipped in any book on the physics of semiconductors. There are many books in which these problems are described, albeit not always so well-chosen and clearly presented as in this one. I should point out the usefulness for solid state physics of Chapter 4, describing approximation methods in quantum mechanics, and Chapter 6 introducing the very important and exciting topic of superconductivity.

Chapters 7-10 provide mainly an introduction to solid state physics dealing with crystalline lattices and symmetries, electron behaviour and motion in a periodical potential, lattice vibrations and phonons, scattering mechanisms and generation-recombination processes. Only in these chapters does the reader find elements of semiconductor physics, like important methods of band structure calculations in semiconductors (Chapter 8), and various generation-recombination mechanisms in semiconductors relevant to optoelectronic applications (Chapter 10). It must be stressed only this part of the content is the type of material one might expect to find in a what is supposed to be a semiconductor physics textbook, and that is what prompts us to question the balance of the book.

Finally, the last four Chapters (11-14) are adequate to the optoelectronic subtitle of the book, being related to the physics of semiconductor devices with an emphasis on optoelectronic applications (though Chapter 14 is devoted to field-effect transistors and typical microelectronic devices). They cover different types of junctions and field-effect structures with application to photonic detectors and light emitters. Semiconductor lasers are among the most important of such topics and it is unfortunate that the author has not paid more attention to them, such as describing their interesting evolution from the simple homojunction lasers to the multiple-quantum-well laser or quantum-cavity laser, and has not indicated contemporary trends in the further evolution to the quantum-dot-array laser. It also seems necessary nowadays to consider recent developments in semiconductor materials and structures leading to blue and ultraviolet optoelectronics.

A valuable feature of the book is the inclusion in every chapter of many interesting examples, problems and homework exercises, though some of them seem to be too difficult.

If, as the author claims in his Preface, this book were to present a wide review of quantum mechanics for the purpose of understanding modern semiconductor devices fabricated using the newest advanced technologies, then it should consistently contain more specific elements of quantum mechanics as well as a more extended description of recently developed quantum semiconductor devices.

Despite the critical remarks above, one must concede that this book may well be a valuable and useful textbook on the physics of semiconductors and semiconductor devices, for not only physics students but more so for engineering students and engineers working in optoelectronics. It is written professionaly in a very competent and clear way. All problems are discussed correctly and presented in an interesting and comprehensive manner with reasonable use of mathematics for quantitative description. I hope that this book will be recognized as a good contribution to the literature of modern semiconductor physics books.