Since the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics.
The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.
Stephen Bruce Sontz received a Ph.D. from the University of Virginia with a dissertation in mathematical physics. He has published around 25 research articles in that field as well as two textbooks with Springer. These are "Quantum Principal Bundles, The Classical Case" and "Quantum Principal Bundles, The Quantum Case". He is a research professor at the Centro de Investigación en Matemáticas, A.C. (CIMAT) in Guanajuato, Mexico. He also teaches undergraduate courses in the Mathematics Department of the University of Guanajuato, where he has given courses using the material in this book.
Introduction to this Path.- Viewpoint.- Neither Particle nor Wave.- Schrödinger's Equation.- Operators and Canonical Quantization.- The Harmonic Oscillator.- Interpreting: Mathematics.- Interpreting: Physics.- The Language of Hilbert Space.- Interpreting: Measurement.- The Hydrogen Atom.- Angular Momentum.- The Rotation Group SO(3).- Spin and SU(2).- Bosons and Fermions.- Classical and Quantum Probability.- The Heisenberg Picture.- Uncertainty (Optional).- Speaking of Quantum Theory (Optional).- Complementarity (Optional).- Axioms (Optional).- And Gravity?.- Measure Theory: A Crash Course.