Non-Relativistic Quantum Theory: Dynamics, Symmetry, and Geometry by Kai S. Lam | (PDF) Free Download

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This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern-Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

User’s Reviews

Editorial Reviews: From the Back Cover This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and ChernSimons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a fine text but not introductory. Some familiarity with the Hilbert Space construct of quantum mechanics is assumed. For example the principle of superposition encodes De Broglie’s discovery and leads to interference effects (particle’s wavefunction interferes with itself-probability density) and in particular motivates the introduction of this vector state space. The linear operators also find their motivation in the vector space construct with certain provisos as well as the need for the field to be complex-Hermitean operators have real eigenvalues(measurements or observations have real values). All this can be found in detail in the introductory chapters of Dirac or Shankar. This being said a rapport with mathematical analysis will also help. The author gives much mathematical detail but doesn’t go as far as Lebesgue integration or finding a countable dense subset to establish separability-Just enough rigor to keep you involved and not chase you away. Covers all material you’d see in a first year graduate course in the first thirty-eight(!)chapters. Particularly good coverage is given of symmetry and group theory(angular momentum, irreducible representations,etc.). I thoroughly enjoyed the chapter on the group theoretic solution of the hydrogen atom problem(Pauli). Neat excercise in commutator algebra between angular momenta and Lenz vector is given-put r in terms of x,y,z! Last part of the book is more of an invitation to differential geometry and topology with applications to quantum theory-get your rigor fix in the math books! Something needs to be said for the introductory chapters. A heuristic but very plausible derivation of the Schroedinger Equation is given via its relation to Hamilton’s formulation. Also perhaps the slickest derivation in quantum mechanics-Dirac’s quantum commutator,Poisson bracket correspondence- comes next. First rate graduate text!

⭐This book includes the derivation of the relationship between the Poisson Bracket and the commutator, which people like to throw around in cite in books, but out of hundreds of books I have seen only this one and Dirac’s pay respect to it. Out of the sections, the ones I can think of that are interesting are the relationship between SO(3) and SU(2), Berry Phase, the matrix mechanics, and the introductory chapter of how Schrodinger derived his equation. It’s nice to have most of the stuff in one place, though the very important omissions are the structure of the wave packet in terms of group velocity and spreading like a heat equation over time. You need that stuff to fully understand QM. For that you can look at Goswami’s Quantum book and Atomic Physics by Max Born. So we are still waiting for a more complete book on QM. Kai writes somewhat in the style of Dirac, though a bit more casual and like a mathematician at times. Dirac was very formal in his development, and started out with intuition to the structure of QM. Kai does not have this much. For intuition you’ll have to seek the other books I recommend, including Dirac.

⭐I’m a mathematician learning quantum mechanics from this book and so far it has been a very good book. He does not skip over many details with the result being that the book is very readable. He also sometimes gives the intuition that lies behind certain results in a way that I have not seen other authors do, which for me gives the book half of its value. For example, rather than simply stating the Schrödinger’s equation and commencing with its study he starts by showing how Schrödinger derived his equation (although I’ve heard that nowadays there is a way of deriving Schrödinger’s equation by studying the geodesics of a spray on a certain infinite dimensional manifold). I wish that there were an appendix that gave a quick review of the prerequisite physics material necessary for this book. Also, I would suggest to the author (and in fact to all authors) that he add to the book more exercises that develop the material of the book in a manner similar to Rotman’s “An Introduction to Algebraic Topology” (that is, exercises that are referenced in later propositions, are simple enough that reader can do, and that give the reader a good familiarity with the definition/concept that was just introduced).

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