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Linearity, Symmetry, and Prediction in the Hydrogen Atom (Undergraduate Texts in Mathematics)
Product Type: Book
Product Price: $59.95
Manufacturer: Springer
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Description
The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, aimed at undergraduate or graduate level students (depending on the college or university), 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 the linear model of quantum mechanics. This method, involving the mathematical area of representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra. Wide applications of this method occur in crystallography, atomic structure, classification of manifolds with symmetry, and other areas.
The topics unfold systematically, introducing the reader first to an important example of a quantum system with symmetry, the single electron in a hydrogen atom. Then the reader is given just enough mathematical tools to make predictions about the numbers of each kind of electronic orbital based solely on the physical spherical symmetry of the hydrogen atom. The final chapters address the related ideas of quantum spin, measurement and entanglement.
This user-friendly exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics. Linearity, Symmetry, and Prediction in the Hydrogen Atom will benefit students in mathematics, physics and chemistry, as well as a literate general readership.
A separate solutions manual is available to instructors.
Reviews
Rating: 5 / 5
Date: 2010-02-24
Summary: "A Chemist's perspective"
For any chemist who is not also mathematically inclined, this book would be very tough going. I minored in math and physics, and I have to admit, I found a lot of this daunting. Ultimately it is very satisfying, though, because while mathematicians like the fact that they can derive properties of the hydrogen atom without recourse to experimental facts and details of chemistry, these very facts and details help a chemist connect to beautiful modern mathematics that would otherwise have no handles for a chemist to grasp.
Singer assumes she is addressing undergraduate mathematics students, and while rigorous at times, she is expansive and gentle in leading the reader through the thickets. It is a very good book, tough but rewarding.
Rating: 5 / 5
Date: 2007-05-03
Summary: "Well done"
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!
Rating: 5 / 5
Date: 2006-06-03
Summary: "A joyful, illuminating book"
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.