# Linearity, Symmetry, and Prediction in the Hydrogen Atom

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August 2005

## Beschreibung

### Beschreibung

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 mechanicsMethod 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

Separate solutions manual available

### Inhaltsverzeichnis

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.### Portrait

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.### Pressestimmen

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)

EAN: 9780387246376

ISBN: 0387246371

Untertitel: 'Undergraduate Texts in Mathema'.
Sprache: Englisch.

Verlag: SPRINGER VERLAG GMBH

Erscheinungsdatum: August 2005

Seitenanzahl: 398 Seiten

Format: gebunden

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