Linearity, Symmetry, and Prediction in the Hydrogen Atom
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Beschreibung
This undergraduate textbook concentrates on how to make predictions about dimensions of the basic states of a quantum system from only two ingredients: the symmetry and the linear model of quantum mechanics. This method, known as representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra and finds wide applications in crystallography, classification of manifolds with symmetry, atomic structure, and so on. The reader is first introduced to an important example of a quantum system with symmetry, the single electron in an hydrogen atom; and 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. This book will benefit students in mathematics, physics and chemistry, as well as a literate general readership.
A separate solutions manual is available to instructors.
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 mechanics Method has wide applications in crystallography, atomic structure, classification of manifolds with symmetry and other areas Engaging and vivid style Driven by numerous exercises and examples Systematic organization
Autor*in
Stephanie Frank Singer
Themen in »Linearity, Symmetry, and Prediction in the Hydrogen Atom«
Abstract algebra Group representation Group theory Quantum mechanics Representation theory hydrogen atom quantum system
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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)
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