Ebook: Linearity, Symmetry, and Prediction in the Hydrogen Atom: an Introduction to Group and Representation Theory

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.;The predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This book 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.