Quantum Mechanics: A Mathematical Introduction (1版)

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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.

The General Theory of Relativity (1版)

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The book aims to expound the general theory of relativity with a mathematical point of view. Catering to the needs of postgraduate students and researchers in the field of astrophysics and mathematical physics, it offers the readers a comprehensive understanding of the advanced topics of the subject matter. It specifically discusses the mathematical foundation of tensor calculus, gives a background of geodesics, Einstein's field equations, linearised gravity, spacetime of spherically symmetric distribution of matter and black holes, and particle and photon orbits in spacetime. Apart from the formulation of general relativity, Lie derivatives and its applications, and causality of spacetime are also discussed in detail. Certain preliminary concepts of extrinsic curvature, Lagrangian formalism of general theory of relativity and 3 + 1 decomposition of space-time are covered and are provided in the book as appendices.

PRINCIPLES OF QUANTUM MECHANICS (2版)

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【原文書】 書名：Principles of Quantum Mechanics 2/e 作者:R. Shankar 出版社：Kluwer Academic Plenum Publishers ISBN：9780306447907 About this Textbook Reviews from the First Edition: "An excellent text … The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist) "No matter how gently one introduces students to the concept of Dirac’s bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin) Reviews of the Second Edition: "This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. … It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews) R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include: - Clear, accessible treatment of underlying mathematics - A review of Newtonian, Lagrangian, and Hamiltonian mechanics - Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates - Unsurpassed coverage of path integrals and their relevance in contemporary physics The requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book’s self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

近代物理導讀與精解 (10版)

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書名：研究所、大學：近代物理導讀與精解 作者：赫龍 出版社：超級科技 出版日期：2014/07/01 ISBN：9785550261682 內容簡介 研究所考試、大學用書,代物理的蓬勃發展，包括愛因斯坦的相對論等，許多理論相繼出籠，全球科技也隨之突飛猛進，尤其是電子科技、光電科技和奈米科技等領域。若想進一步鑽研這些領域，對近代物理的了解更是不可或缺。

RELATIVITY : THE SPECIAL & THE GENERAL THEORY

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書名：Relativity: The Special & The General Theory 作者：EINSTEIN 出版社：PRINCETON 出版日期：2019/03/12 ISBN：9780691191812

Gravity: An Introduction to Einstein`s General Relativity (1版)

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Gravity: An Introduction to Einstein`s General Relativity +作者：Hartle +年份：2021 年1 版 +ISBN：9781316517543 +書號：PH0176H +規格：精裝/單色 +頁數：608 +出版商：Cambridge 'Physics-first' approach, so relevant simple solutions of the Einstein equation are presented first, before introducing the field equations of general relativity and their supporting mathematics, brings the student to the heart of the physical phenomena as quickly as possible Novel and simple examples are used to keep the presentation concise and accessible, for instance, Schwarzschild black holes, spherical stars, weak gravitational waves in flat spacetime Only absolutely essential new mathematical concepts are introduced, and these only when needed, to make GR accessible to physics students with typical calculus knowledge Layered structure and included course map allow the text to be used for a range of course lengths and levels, from junior level to introductory graduate level in physics and astronomy 目錄 Part I. Space and Time in Newtonian Physics and Special Relativity: 1. Gravitational physics 2. Geometry as physics 3. Space, time, and gravity in Newtonian physics 4. Principles of special relativity 5. Special relativistic mechanics. Part II. The Curved Spacetimes of General Relativity: 6. Gravity as geometry 7. Description of curved spacetime 8. Geodesics 9. The geometry outside a spherical star 10. Solar System tests of general relativity 11. Relativistic gravity in action 12. Gravitational collapse and black holes 13. Astrophysical black holes 14. A little rotation 15. Rotating black holes 16. Gravitational waves 17. The universe observed 18. Cosmological models 19. Which universe and why?. Part III. The Einstein Equation: 20. A little more math 21. Curvature and the Einstein equation 22. The source of curvature 23. Gravitational wave emission 24. Relativistic stars Appendix A. Units Appendix B. Curvature quantities Appendix C. Curvature and the Einstein equation Appendix D. Pedagogical strategy

Gravity: An Introduction to Einstein`s General Relativity (1版)

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書名：Gravity: An Introduction to Einstein`s General Relativity (PNIE) 作者：Hartle 出版社：Pearson 出版日期：2014/00/00 ISBN：9781292039145 內容簡介 ●Examples come first, derivations later. In this "physics first" approach, relevant simple solutions of the Einstein equation are presented first, before introducing the field equations of general relativity and their supporting mathematics. This brings the student to the heart of the physical phenomena as quickly as possible. ●The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. Global positioning system, black holes, X-ray sources, pulsars, quasars, gravitational waves, the big bang, and the large scale structure of the universe, for example, are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. ●Novel and simple examples are presented to keep the presentation concise and accessible: for instance, Schwarzschild black hole, spherical stars, weak gravitational waves in flat spacetime. ●Mathematics, beyond the typical advanced calculus knowledge, is kept to a minimum. Only absolutely essential new mathematical concepts are introduced, and these only when needed. ●The text's layered structure allows the text to be used for a range of courses depending on the length and level of the course—from junior level to introductory graduate level in physics and astronomy. After just the first few chapters, a student will take away a broad introduction to some of the basic phenomena of gravitational physics, and not just mathematical tools. ●Illustrative boxes are interspersed throughout, providing students with applications, experiments, ideas, examples, and interesting sidelights that extend and complement concepts presented in the basic text without interrupting its flow. 目錄 I. SPACE AND TIME IN NEWTONIAN PHYSICS AND SPECIAL RELATIVITY. 1. Gravitational Physics. 2. Geometry as Physics. 3. Space, Time, and Gravity in Newtonian Physics. 4. Principles of Special Relativity. 5. Special Relativistic Mechanics. II. THE CURVED SPACETIMES OF GENERAL RELATIVITY. 6. Gravity as Geometry. 7. The Description of Curved Spacetime. 8. Geodesics. 9. The Geometry Outside a Spherical Star. 10. Solar System Tests of General Relativity. 11. Relativistic Gravity in Action. 12. Gravitational Collapse and Black Holes. 13. Astrophysical Black Holes. 14. A Little Rotation. 15. Rotating Black Holes. 16. Gravitational Waves. 17. The Universe Observed. 18. Cosmological Models. 19. Which Universe and Why? III. THE EINSTEIN EQUATION. 20. A Little More Math. 21. Curvature and the Einstein Equation. 22. The Source of Curvature. 23. Gravitational Wave Emission. 24. Relativistic Stars.

Einstein’s Relativity in Great Britain: From Eddington to Hawking and Penrose. a Tale of Physicists, Astronomers, Mathematicians and Philosophers (1版)

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【簡介】 Soon after their publication (1905, 1915), Einstein’s special and general theories of relativity received attention by a wide variety of British scholars (astronomers, physicists, mathematicians and philosophers). That reaction varied from deep acceptance (as was the case of Arthur Eddington) to straightforward opposition. This book analyzes those reactions, which involved a large number of important scientists as well as philosophers, like Bertrand Russell or Alfred N. Whitehead. The study will cover from the 1910s till the 1960s, when the work of a group of relativists centered in London and Oxford (Penrose), Cambridge (Sciama and Hawking) as well as the Bondi’s group at King’s College London, who finally introduced a new, global approach to general relativity.