Quantum mechanics : a mathematical introduction
著者
書誌事項
Quantum mechanics : a mathematical introduction
Cambridge University Press, 2023
- :hbk.
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注記
Includes bibliographical references (p.368-374) and index
内容説明・目次
内容説明
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 Schroedinger 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.
目次
- 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.
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