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 379384) 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 
