Undergraduate Texts in Mathematics: Linearity, Symmetry, and Prediction in the Hydrogen Atom (Hardback)

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LIKE NEW: This book is in excellent, like-new condition. It was printed on acid-free paper.

Product Details

This volume is part of Springer'sUndergraduate Texts in Mathematics series.

Also from the back cover: "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 systems 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."

Chapters

1. Setting the Stage
2. Linear Algebra over the Complex Numbers
3. Complex Scalar Product Spaces (a.k.a. Hilbert Spaces)
4. Lie Groups and Lie Group Representations
5. New Representations from Old
6. Irreducible Representations and Invariant Integration
7. Representations and the Hydrogen Atom
8. The Algebra so(4) Symmetry of the Hydrogen Atom
9. The Group SO(4) Symmetry of the Hydrogen Atom
10. Projective Representations and Spin
11. Independent Events and Tensor Products

Appendices

1. Spherical Harmonics
2. Proof of the Correspondence between Irreducible Linear Representations of SU(2) and Irreducible Projective Representations of SO(3)
3. Suggested Paper Topics

The textbook ends with Bibliography, Glossary of Symbols and Notation, and Index. A separate solutions manual for instructors is available from the publisher.