Linearity, Symmetry, and Prediction in the Hydrogen Atom

• Main Author: Singer, Stephanie Frank (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Physics.; Group theory.; Applied mathematics.; Engineering mathematics.; Mechanics.; Elementary particles (Physics).; Quantum field theory.; Atoms.; Atomic, Molecular, Optical and Plasma Physics.; Elementary Particles, Quantum Field Theory.; Group Theory and Generalizations.; Mathematical Methods in Physics.; Applications of Mathematics.

This is a textbook for a senior-level undergraduate course for math, physics and chemistry majors. This one course can play two different but complimentary roles: it can serve as a capstone course for students finishing their education, and it can serve as motivating story for future study of mathem...

Table of 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.