Navigating Solutions for Mark Fox's Optical Properties of Solids
The textbook by Mark Fox is one of the more widely used references for graduate-level solid state optics courses. It covers band structure, dielectric response, phonon interactions, excitons, and quantum confinement among other topics. The problem sets at the end of each chapter are where most students actually encounter difficulty, and having access to worked solutions can save weeks of frustration. A proper solution manual does exist for this book, published alongside the second edition. It covers roughly two-thirds of the problems with step-by-step derivations. You can typically find it through academic publishers or university library systems. However, what many students actually end up using are the solutions circulating through physics departments, Stack Exchange threads, and research group websites. These vary wildly in quality. I ran into this myself when I was working through Chapter 5 on interband transitions. The published manual skips several derivations that assume familiarity with k dot p perturbation theory, and the online solutions I found were riddled with sign errors in the dipole matrix element calculations. What I ended up doing was cross-referencing at least three independent sources and then verifying each result against the experimental data the book cites. That process took about four hours for a single problem set that the textbook suggests is a few days' work.
How to Actually Use These Solutions Effectively
Here is the practical approach. Work the problem on your own first, even if you get stuck partway through. Write down where you stop. Then consult the solution and trace your steps against theirs. If their method is completely different from yours, figure out why. Most of the problems in this book can be attacked from more than one angle, and recognizing those alternative paths is where the actual learning happens. The dielectric function derivations in Chapters 3 and 4 are the ones that trip people up most. The textbook uses the Lorentz oscillator model and then builds from there into the Kane model for semiconductors. I have seen students spend enormous time on these because they skip the underlying assumption that the electron-phonon coupling term is treated as a perturbation. If you do not carry that approximation through consistently, your final expression for the complex permittivity will diverge from the textbook answer, and you will not know where you went wrong. The workaround is to work backwards from the final form of the dielectric function and identify which term each physical effect contributes to.
A Specific Edge Case That Costs People Points
Problem 7.3 in the second edition asks about quantum well absorption edge shifts. The solution assumes a simple infinite well approximation, but the actual exercise expects you to account for the finite barrier height. Several solution sets online miss this entirely and give the infinite well answer, which is wrong for the stated problem. When I worked through it, I had to solve the transcendental equation for the finite square well eigenvalues numerically. I used a simple bisection method in Python, iterating until the energy converged to within 0.001 eV. That extra step changed the absorption edge prediction by about 12 percent compared to the infinite well result, which is significant if you are modeling actual semiconductor heterostructures. Fox does an adequate job with classical and semi-classical treatments of optical response. The treatment of excitonic effects is thorough. Where the book becomes limited is in modern topics like plasmonics, metamaterials, and topological insulators. If your course covers those areas, you will need supplementary references. The solutions to the later chapters often assume knowledge that the book itself does not fully develop. For students working through this material independently, the most efficient path is to pair the Fox solutions with Ashcroft and Mermin for the solid state fundamentals, and Kittel for crystal optics. Having those references side by side lets you verify that the approximations Fox makes are justified in each context rather than just accepting them on authority.
Get the Full Details
Practical Notes on Accessing Solutions
University libraries often hold the official solution manual in reserve collections. If you are a student, check with your departmental liaison librarian first. Online forums like Physics Stack Exchange have active threads for specific problems, but the answers are scattered and uncurated. ResearchGate sometimes has uploads from course instructors, though the quality is inconsistent. Avoid automated PDF generators that claim to have complete solutions, as these frequently contain copied errors from earlier attempts that propagate through multiple versions. The problems that matter most for exam preparation are the ones involving the joint density of state calculations and the absorption coefficient derivations. Mastering those two areas will cover roughly half the calculation-based questions you will encounter in a standard graduate optics exam on this material.
