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Book Cover
E-book
Author Singer, Stephanie Frank, 1964-

Title Linearity, symmetry, and prediction in the hydrogen atom / Stephanie Frank Singer
Published New York : Springer, [2005]
©2005
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Description 1 online resource (xiv, 396 pages) : illustrations
Series Undergraduate texts in mathematics
Undergraduate texts in mathematics.
Contents Setting the stage -- Linear algebra over the complex numbers -- Complex scalar product spaces (a.k.a. Hilbert spaces) -- Lie groups and lie group representations -- New representations from old -- Irreducible representations and invariant integration -- Representations and the hydrogen atom -- The algebra so(4) symmetry of the hydrogen atom -- The group SO(4) symmetry of the hydrogen atom -- Projective representations and spin -- Independent events and tensor products
Summary "The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, which is 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." "This 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."--Jacket
Bibliography Includes bibliographical references (pages 379-384) and index
Subject Group theory.
Hydrogen.
Atoms.
Linear algebraic groups.
Symmetry (Physics)
Representations of groups.
Quantum theory.
Form Electronic book
LC no. 2005042679
ISBN 0387246371 (alk. paper)
0387263691
661133470X
9780387246376 (alk. paper)
9780387263694
9786611334703