Linearity, Symmetry, and Prediction in the Hydrogen Atom

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 mechanics

Method 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

Autorentext

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.

Inhalt

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.