Quantum Mechanics: A Mathematical Introduction

by Andrew J. Larkoski

Overview

This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basis of modern physics research are also included, such as the density matrix, entropy, and measures of entanglement. Written for an undergraduate audience, this book offers a unique and mathematically self-contained treatment of this hugely important topic. Students are guided gently through the text by the author's engaging writing style, with an extensive glossary provided for reference and numerous homework problems to expand and develop key concepts. Online resources for instructors include a fully worked solutions manual and lecture slides.

Product Details

ISBN-13:	9781009100502
Publisher:	Cambridge University Press
Publication date:	12/15/2022
Pages:	398
Sales rank:	774,059
Product dimensions:	7.20(w) x 10.28(h) x 0.91(d)

About the Author

Andrew J. Larkoski is Acting Assistant Professor at SLAC National Accelerator Laboratory. He earned his Ph.D. from Stanford University and has held research appointments at Massachusetts Institute of Technology and Harvard University, and he was also a Visiting Assistant Professor at Reed College. A leading expert on particle physics, he has published over fifty articles, and won the LHC Theory Initiative Fellowship and the Wu-Ki Tung Award for Early-Career Research on QCD. His previous textbook with Cambridge, Elementary Particle Physics: An Intuitive Introduction (2019), offers a modern and accessible introduction to the guiding principles of particle physics.

Table of Contents

1. Introduction; 2. Linear Algebra; 3. Hilbert Space; 4. Axioms of Quantum Mechanics and Their Consequences; 5. Quantum Mechanical Example: The Infinite Square Well; 6. Quantum Mechanical Example: The Harmonic Oscillator; 7. Quantum Mechanical Example: The Free Particle; 8. Rotations in Three Dimensions; 9. The Hydrogen Atom; 10. Approximation Techniques; 11. The Path Integral; 12. The Density Matrix; 13. Why Quantum Mechanics?; Appendix A. Mathematics Review; Appendix B. Poisson Brackets in Classical Mechanics; Appendix C. Fundamental Constants and Units; Appendix D. Quantum Mechanics Jargon Glossary; Appendix E. Bibliography.

Editorial Reviews

‘This book is a refreshing and innovative addition to quantum mechanics teaching. It will help students build strong mathematical skills to rely on when studying this novel subject. Larkoski demystifies the subject and provides instructors with new ways to cover even the most canonical examples in quantum mechanics. I think it will also be a very useful companion for students learning quantum field theory.' Seyda Ipek, Carleton University, Ottawa

‘Larkoski's book uses an original and innovative approach to introduce (and develop intuition about) the mathematics leading to the axioms of quantum mechanics. Overall, a refreshing introduction to quantum mechanics.' Jean-Sebastien Gagnon, Norwich University, Vermont

‘Dr Larkoski starts with a gentle introduction to linear algebra and the Dirac – von Neumann axioms of quantum mechanics. Throughout he stresses the role of the scientific method in which measurable states and observables evolve and predictions of this evolution become tests of the model hypothesis. Dr Larkoski strives to keep differential equations to a minimum by exploiting symmetries and conservation laws through Lie algebra and group properties. Students see standard one-dimensional examples typically encountered in an undergraduate course. The 3D hydrogen Hamiltonian is diagonalized interestingly using angular momentum and Laplace – Runge – Lenz operators. Advanced topics are introduced including perturbation theory, WKB approximation, path integrals, the density matrix, and entanglement.' Russell Herman, University of North Carolina, Wilmington

‘Quantum Mechanics by Larkoski is a much-needed update to undergraduate quantum mechanics teaching, and a good introduction to the way physicists think about and use quantum mechanics. Indispensable tools of modern research like the density matrix, s-matrix and Lie algebras are introduced and applied to the analysis of pedagogical systems, elucidating their meaning and functionality. The book is also well written and generally easy to follow, with appropriately placed examples.' Varun Makhija, University of Mary, Washington

From the Publisher