Topics in Advanced Quantum Mechanics (Dover Books on Physics) by Barry R. Holstein (PDF)

Description

This graduate-level text is a product of the author’s course in advanced quantum mechanics, taught many times at the University of Massachusetts, Amherst. It offers students a thorough grounding in nonrelativistic techniques related to its full relativistic treatment, including material on nonrelativistic Feynman diagrams and their application to electromagnetic process.Topics include propagator methods, scattering theory, charged particle interactions and their applications, alternate approximate methods, and the Klein-Gordon and Dirac equations. Problems appear in the flow of the discussion, rather than at the end of chapters. An abundance of content makes this text more than adequate for single-semester courses, and supplemental material — designated by an asterisk — is provided for dedicated readers.

User’s Reviews

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⭐written review

⭐The author: “I find in this ability to examine the same result from new and differing points of view a real sense of understanding and satisfaction, and it is my hope that other students of the subject may experience the same.” This is one of my favorite textbooks, as it achieves that aim–of examining a result from multiple perspectives. Anyone familiar with the numerous American Journal of Physics articles written by Professor Holstein ascertains that he keeps the reader always uppermost in mind when presenting his material. His ability to distill advanced material in a manner digestible to the neophyte is example for all.(1) This book of ‘topics’ in advanced quantum mechanics should be preceded by a standard text, such as Merzbacher (Quantum Mechanics). If such is the case, the student will be prepared to tackle the material here. Appearances of mathematical complexity belie the copious physical dexterity espoused. Mathematics is kept reasonable as few intermediate steps are omitted. Propagator methods (Feynman and Green) chapter one can hardly be improved upon: already (page 30) the reader understands how to use the prescription “sum over paths” alongside diagrammatic techniques.(2) Chapter two begins a deeper discussion of scattering theory (a useful exercise: compare page 51 here, to the analogous derivation on page 66 of Sakurai ,1967). As done here, and throughout, the reader is first presented with an approach based on physical intuition following which is a more rigorous discussion. Many topics are given then (at least) two explorations. The discussion of scattering theory is a highlight. If it were possible to give a simpler exposition of Lagrangian formalism and electrodynamics, I would be surprised. Especially, gauge invariance and the Aharonov-Bohm effect–compare to Sakurai !(3) Chapter three, concludes with vacuum energy and Casimir effect. The next chapter, applying what one has learned in the previous three chapters to charged particle interactions, is a tour de force. Note this Problem 5.1, Why Is The Sky Blue? Here we learn of Compton scattering, Lamb shift calculation (first intuitively, then more formally !), dispersion relations (intuitive, then formal !). Onward to effective Lagrangians. Continuing with fifth chapter–alternative approximation methods–again, it is difficult to point to a more detailed, clear presentation of WKB, semiclassical and adiabatic approximations. Next, equations of Klein-Gordon (patterned after Gordon Baym’s lectures) followed by Dirac equation. Primarily a pedagogic perspective, those equations (as detailed in chapters six and seven) are made as effortless and explicit as one is likely to find elsewhere.(4) Final Chapter, Advanced Topics: radiative corrections, spinless particles, path Integrals in quantum field theory, strong interactions. Suffice it to say, if the student has progressed this far in the text, advanced will appear to be much less advanced ! I’ve ignored much in this review (great exercise-problem sets and functional techniques, for instance). Hopefully, this text will become part of one’s personal library. Keep paper and pencil handy for fascinating work. This helpful resource deserves wide readership.Addendum:Barry Holstein, 2019 Herman Feshbach Prize in Theoretical Nuclear Physics Recipient, “For seminal theoretical studies of fundamental symmetries in nuclei, including radioactive nuclear decays, parity-violating nucleon-nucleon interactions, and chiral dynamics of mesons and baryons.”

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