Applied Quantum Mechanics , A. F. J. Levi Cambridge U. Press, New York, 2003. $130.00, $55.00 paper (523 pp.). ISBN 0-521-81765-X, ISBN 0-521-52086-X paper, CD-ROM
Teaching graduate-level quantum mechanics to engineering students is a significant challenge. The barriers do not lie where one might expect in the conceptual difficulties of indeterminacy and wave–particle duality but rather in the fact that the subject does not lend itself to the large volume of homework problems those students expect. Moreover, the fraction of the engineering curriculum that can be devoted to quantum mechanics is limited by the need to present other levels of abstraction of modern technology, such as circuits and systems. In the typical physics curriculum, mastery of nonrelativistic quantum mechanics requires not only two semesters of the topic itself, but also two semesters of mathematical methods. Engineering curricula, however, cannot commit that many classes to teaching quantum mechanics.
Anthony Levi’s Applied Quantum Mechanics is a significant contribution to solving the problems mentioned above. The author addresses parts of the subject that are important to terrestrial, low-energy technologies. In contrast to a textbook aimed at physics students, Levi’s book devotes minimal attention to problems such as atomic structure and scattering from spherical potentials. The text focuses on electron systems that may be described in one dimension, such as bound and extended states; on the harmonic oscillator as a model for collective modes including photons and phonons; and on perturbation theory, with discussions on Fermi’s golden rule for stimulated optical transitions. The author also presents equilibrium statistical mechanics, a necessary element of any engineering application. In a very nice touch, he uses the semiconductor diode laser as the primary example of how quantum mechanics is applied. The device depends upon essentially all of the topics covered in the book. Although Levi only considers a simple model of the diode laser, presenting the device as a target application gives an instructor the opportunity to motivate students into examining the book’s topics.
The first chapter is a review of classical mechanics and electromagnetism, but the author chooses examples that have relevance to quantum systems. For example, the linear chain of masses coupled by springs introduces the notion of nonlinear dispersion (frequency versus wavevector) relations. In later parts of the chapter, Levi includes discussions of classical systems, such as photonic crystals, that share a mathematical foundation with the quantum systems that are the focus of the text.
The book comes with a CD-ROM that contains MATLAB code for a number of examples and exercises; the book also introduces elementary numerical techniques for dealing with quantum problems. The inclusion of numerical techniques significantly increases the number of problems the student can solve with reasonable amounts of effort. It also offers readers a much more realistic appreciation of the way quantum systems must be analyzed in practical technological applications.
One frustrating aspect of the book is that, on some occasions, Levi develops the background for a significant result but then fails to follow through to the result itself. An example is his treatment of the dynamics of electrons in crystals, including the effects of the complicated dispersion relation, or band structure. At various points, the author mentions group velocity and describes band structures, but he never explicitly states the group-velocity and acceleration theorems that determine the electron dynamics.
A novel feature of Applied Quantum Mechanics is the inclusion of solutions for all the exercises. I am not quite sure how this will work in the context of a course taken for credit. Because the answers are readily accessible, instructors will need to either supplement the problems given in the text or modify their grading algorithms.
In summary, Levi’s book represents a very large step in the right direction for teaching quantum mechanics to engineering students. I have adopted it as the textbook for my next class on the subject. However, I believe we ultimately need an even more radical departure from the traditional physics curriculum textbook.