Waves and Oscillations: A Prelude to Quantum Mechanics [Repost]

Waves and oscillations permeate virtually every field of current physics research, are central to chemistry, and are essential to much of engineering. Furthermore, the concepts and mathematical techniques used for serious study of waves and oscillations form the foundation for quantum mechanics. Once they have mastered these ideas in a classical context, students will be ready to focus on the challenging concepts of quantum mechanics when they encounter them, rather than struggling with techniques.

This lively textbook gives a thorough grounding in complex exponentials and the key aspects of differential equations and matrix math; no prior experience is assumed. The parallels between normal mode analysis, orthogonal function analysis (especially Fourier analysis), and superpositions of quantum states are clearly drawn, without actually getting into the quantum mechanics. An in-depth, accessible introduction to Hilbert space and bra-ket notation begins in Chapter 5 (on symmetrical coupled oscillators), emphasizing the analogy with conventional dot products, and continues in subsequent chapters.

Connections to current physics research (atomic force microscopy, chaos, supersolids, micro electro-mechanical systems (MEMS), magnetic resonance imaging, carbon nanotubes, and more) are highlighted in the text and in end-of-chapter problems, and are frequently updated in the associated website.

The book actively engages readers with a refreshing writing style and a set of carefully applied learning tools, such as in-text concept tests, "your turn" boxes (in which the student fills in one or two steps of a derivation), concept and skill inventories for each chapter, and "wrong way" problems in which the student explains the flaw in a line of reasoning. These tools promote self-awareness of the learning process.

The associated website features custom-developed applets, video and audio recordings, additional problems, and links to related current research. The instructor-only part includes difficulty ratings for problems, optional hints, full solutions, and additional support materials.


Reader's review

(…) I taught a college sophomore-level class on Vibrations, Waves, and Optics for three years. For such a class, my department likes to teach with a mathematical background which makes use of complex variables and basic linear algebra (i.e. the ability to manipulate matrices and the ability find and use eigenvectors and eigenvalues). In my view, a class (and text) like this should fulfill two objectives: (1) it should teach applied Fourier analysis (and Fourier analysis's application to as wide a spectrum of examples as possible); and, (2) it should prepare the students for their first serious course on Quantum Mechanics. As much as possible, the course and text should introduce the mathematics and concepts that the students will encounter in quantum mechanics in a classical context. This second objective makes the transition to quantum mechanics as lucid as possible so that students are grappling with the parts of Quantum Mechanics which are truly surprising and not the parts that are just due to the wave nature of the wave functions. Walter Fox Smith's text achieves both of these objectives and does so well.

I spent the first couple of years that I taught the class looking for a text which fulfilled these objectives and did so with the level of mathematical sophistication that I wanted in my class. In general, the texts that I found before the publication of Smith's text were terrible: the students (and I) found the texts hard to read and hard to learn from. Smith's text organizes the material in a way that is easier to learn than from the books that I found previously.(…)