Linearity, Symmetry, and Prediction in the Hydrogen Atom : Undergraduate Texts in Mathematics - Stephanie Frank Singer

Linearity, Symmetry, and Prediction in the Hydrogen Atom

By: Stephanie Frank Singer

Hardcover | 9 August 2005

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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.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. The Hydrogen Atom: An Introduction to Group and Representation Theory will benefit students in mathematics, physics and chemistry, as well as a literate general readership. A separate solutions manual is available to instructors.
Industry Reviews

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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Published: 1st December 2010

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