Linearity, Symmetry, and Prediction in the Hydrogen Atom (Undergraduate Texts in Mathematics) 2005th Edition by Stephanie Frank Singer (PDF)

Description

Concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ingredients: the symmetry and linear model of quantum mechanicsMethod has wide applications in crystallography, atomic structure, classification of manifolds with symmetry and other areasEngaging and vivid styleDriven by numerous exercises and examplesSystematic organizationSeparate solutions manual available

User’s Reviews

Editorial Reviews: Review From the reviews:”Here is another book which is centered around the SO(4)-invariance of the 1/r potential. … the present author always remains on a very solid mathematical ground. … The author prepares carefully the mathematical ingredients (Hilbert spaces, Lie groups, Lie algebras, representations). The style of this senior-level undergraduate text is very fluent and – in the best sense – entertaining.” (Evelyn Weimar-Woods, Zentralblatt MATH, Vol. 1088 (14), 2006)”It is an introductory textbook on the unitary representation theory of Lie groups, with emphasis on the important groups SO (3), SU (2), and SO (4), with the hydrogen atom as a motivating, unifying theme. The intended audience is senior-level undergraduate majors in mathematics, physics, and chemistry. Numerous exercises are provided. … will recommend the book as supplementary reading to those students who desire to understand the mathematics at a deeper level. … Singer’s book is a very good one for undergraduate mathematics majors.” (Stephen A. Fulling, American Mathematical Monthly, Vol. 114, August-September, 2007) About the Author Stephanie Frank Singer received her Ph.D. in Mathematics from the Courant Institute in 1991. In 2002 she resigned her tenured professorship at Haverford College. Since then she has been writing and consulting independently. Her first book was Symmetry In Mechanics: A Gentle, Modern Introduction.

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

⭐BUY THIS BOOK if you’re a physicist or student of physics (or any allied discipline) who feels a little uneasy about the mathematics of nonrelativistic quantum mechanics—tensor products and Lie algebra representations and all that. Ignore the title. This book is about the mathematics of quantum mechanics and only occasionally and briefly touches on the hydrogen atom for illustrative purposes. Instead, this book is a pedagogical gem when it comes to the mathematics you so much need to know, but can rarely find presented clearly. Trust me: if you work your way through this book, you’ll come out the other side confident in your mastery of these topics of central importance. And you’ll enjoy the journey. I’ve sampled many a text on these topics. This is far and away the best. Do it now, and you’ll be glad you did: BUY THIS BOOK! (If you’re wondering, I have no connection whatsoever with the author, who dropped out of the field long ago.)

⭐The idea of the book is great, but there are just so many blatant errors throughout it—many in the chapters as well as the 3 in the exercises so far. An exercise I was just doing said to prove that 2 x 2 diagonal special unitary matrices is isomorphic to T X T, which is not true! It’s isomorphic to one copy of the circle group.

⭐I bought this book at the Stanford bookstore a few days ago because it so closely matched what I was thinking of trying to understand myself, namely, how hard is it to go from the basic principles of quantum mechanics and recover experimental results about atoms. Well, the simplest atom is the hydrogen atom, and this book does the all the math associated with the s-shells, p-shells, energy levels, and so on, and it does so without bringing in extra physics or chemistry that a person is supposed to take on faith. If you’re a mathematician who already knows some group representation theory (through Lie algebras, say), this book gives a particularly rapid path to understanding why the physicists find it so useful!

⭐Although I’ve taught quantum mechanics many times, I am learning a great deal from this splendid book. I much admire the care and consideration Singer has devoted to helping readers comprehend and enjoy fascinating, fundamental material. I hope she writes more such exceptional, mind-opening books! Dudley Herschbach, Prof. of Chemistry Harvard & Prof. of Physics, Texas A & M Univ.

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