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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.
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.
Description
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.
