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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010301092 | QC174.12 G58 2012 | Open Access Book | Book | Searching... |
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Summary
Summary
This slim volume covers the traditional parts of quantum mechanics: semiclassical theories of radiation and scattering, a number of advanced problems: Feynman diagrams and relativistic quantum mechanics and a collection of modern items: superfluidity and high-temperature superconductivity. The book begins with the description of the basic principles of mechanics, electrodynamics and quantum mechanics, which are needed for understanding the subsequent chapters. Qualitative methods (analytical properties and paradoxes in quantum mechanics) are also introduced. This useful textbook also pairs the problems with their solutions.
Reviews 1
Choice Review
This tour of quantum mechanics by Gitterman (Bar Ilan Univ., Israel) is indeed quite brief; at 130 pages, including the index, it is a very slim volume. This is far less than other books that cover the same material, which corresponds roughly to courses in the second or third semester of US graduate programs in physics. The selection of topics is good. Beginning chapters include "Semiclassical Theory of Radiation," "Many-Body Problem," and "S-matrix, Green Function, and Feynman Diagrams." Later chapters discuss relativistic quantum mechanics, semiclassical techniques, and scattering theory and analytic properties. The final chapter discusses paradoxes in quantum theory. Most chapters have a few worked problems. Topic treatments are straightforward, but their simplicity can be deceiving. For example, the treatment of the Casimir effect expresses a divergent sum over zero-point energies in terms of zeta(-3) without any mention of the conceptual difficulties or even any mathematical detail. Some talented and motivated students will love the presentation, but many will be unable to fill in the gaps themselves. Faculty will find the text useful in preparing lectures in graduate quantum mechanics courses. Graduate students might find it helpful for self-study and preparation for comprehensive exams. Summing Up: Recommended. Graduate students and faculty. M. C. Ogilvie Washington University
Table of Contents
| Preface | p. v |
| 1 Introduction | p. 1 |
| 1.1 Classical mechanics | p. 1 |
| 1.1.1 Newton's law | p. 1 |
| 1.1.2 Principle of least action | p. 2 |
| 1.1.3 Hamilton's equations | p. 3 |
| 1.1.4 Hamilton-Jacobi equation | p. 4 |
| 1.2 Electrodynamics | p. 5 |
| 1.2.1 Maxwell's equations | p. 5 |
| 1.2.2 Electromagnetic potentials | p. 7 |
| 1.2.3 Lagrangian for the electromagnetic field | p. 9 |
| 1.3 Quantum mechanics | p. 10 |
| 1.3.1 Wave function | p. 10 |
| 1.3.2 Dynamic behavior | p. 11 |
| 1.3.3 Conservation laws in quantum mechanics | p. 12 |
| 1.3.4 Different representations | p. 14 |
| 1.3.5 Aharonov-Bohm effect | p. 14 |
| 2 Semiclassical Theory of Radiation | p. 17 |
| 2.1 Fermi's Golden Rule | p. 17 |
| 2.2 Dipole transitions | p. 19 |
| 2.3 Forbidden and strictly forbidden transitions | p. 20 |
| 2.4 Selection rules | p. 21 |
| 2.5 Radioactivity | p. 21 |
| 2.6 Photoelectric effect | p. 22 |
| 2.7 Cherenkov effect | p. 23 |
| 2.8 Compton effect | p. 24 |
| 2.9 Problems | p. 25 |
| 3 Many-body Problem | p. 29 |
| 3.1 Fermions and bosons | p. 29 |
| 3.2 N-representation | p. 30 |
| 3.3 Lagrangian and Hamiltonian of quantum systems | p. 31 |
| 3.4 Second quantization | p. 31 |
| 3.5 Hamiltonian in second quantization | p. 32 |
| 3.6 Quantization of the electromagnetic field | p. 34 |
| 3.7 Full quantum mechanical description of the particle-wave interaction | p. 36 |
| 3.8 Superfluidity and superconductivity | p. 38 |
| 3.8.1 Statistics of a bosonic gas | p. 39 |
| 3.8.2 Microscopic theory of superfluidity | p. 40 |
| 3.8.3 Experimental detection of superfluidity | p. 42 |
| 3.8.4 Electron pairing in superconductors | p. 43 |
| 3.8.5 Microscopic theory of superconductivity | p. 45 |
| 3.8.6 High-temperature superconductivity | p. 46 |
| 3.9 Problems | p. 48 |
| 4 S-matrix, Green Function, Feynman Diagrams | p. 51 |
| 4.1 S-matrix | p. 51 |
| 4.2 Green function | p. 52 |
| 4.3 Green function in second quantization | p. 54 |
| 4.4 Wick theorem | p. 55 |
| 4.5 Feynman diagrams | p. 56 |
| 4.5.1 Electrons in an external field | p. 58 |
| 4.5.2 Hartree and Hartree-Fock approximations | p. 59 |
| 4.5.3 Electron gas at low and high density | p. 60 |
| 4.6 Problems | p. 63 |
| 5 Relativistic Quantum Mechanics | p. 65 |
| 5.1 Klein-Gordon equation | p. 65 |
| 5.2 Dirac equation | p. 66 |
| 5.3 Dynamic solution of the Dirac equation | p. 67 |
| 5.4 Electron spin | p. 69 |
| 5.5 Dirac equation for a free particle | p. 71 |
| 5.6 Motion in a central field | p. 72 |
| 5.7 Nature of the physical vacuum | p. 75 |
| 5.7.1 Lamb shift | p. 76 |
| 5.7.2 Klein paradox | p. 77 |
| 5.7.3 Casimir force | p. 78 |
| 5.8 Problems | p. 80 |
| 6 Semiclassical Approximation to Quantum Mechanics | p. 83 |
| 6.1 Wave equation | p. 83 |
| 6.2 Turning points | p. 85 |
| 6.3 Energy spectrum | p. 86 |
| 6.4 Tunneling through a potential barrier | p. 88 |
| 6.5 Problems | p. 90 |
| 7 Scattering | p. 95 |
| 7.1 Phenomenological description of scattering | p. 95 |
| 7.2 Born approximation | p. 96 |
| 7.3 Scattering by different potentials | p. 98 |
| 7.4 Partial waves | p. 99 |
| 7.5 Optical theorem | p. 101 |
| 7.6 Problems | p. 103 |
| 8 Analytical Properties | p. 109 |
| 8.1 Analytical properties of the wave function | p. 109 |
| 8.2 Analytical properties of the scattering amplitude | p. 110 |
| 8.3 Resonance scattering | p. 111 |
| 8.4 Symmetry | p. 112 |
| 8.4.1 Parity | p. 112 |
| 8.4.2 Conservation laws | p. 113 |
| 8.4.3 Degeneracy | p. 114 |
| 8.4.4 Internal symmetries | p. 115 |
| 8.4.5 Complex conjugation and time reversal | p. 115 |
| 8.4.6 Gauge transformation | p. 116 |
| 9 Paradoxes in Quantum Mechanics | p. 119 |
| 9.1 Schrödinger's cat | p. 119 |
| 9.2 The Einstein-Podolsky-Rosen (EPR) paradox | p. 120 |
| 9.3 Hidden variables and Bell's inequality | p. 122 |
| Bibliography | p. 127 |
| Index | p. 129 |
