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Quantum Mechanics: Fundamentals,9780387955766
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Quantum Mechanics: Fundamentals


Author(s): Gottfried, Kurt; Yan, Tung-Mow
ISBN10:  0387955763
ISBN13:  9780387955766
Format:  Hardcover
Pub. Date:  8/1/2003
Publisher(s): Springer Verlag

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SummaryTable of Contents
This classic text provides a comprehensive exposition of the concepts and techniques of quantum mechanics. The phenomena treated are sufficiently simple to allow the student to readily assess the validity of the models so that attention is not deflected from the heart of the subject. To that end, the book concentrates on systems that can either be solved exactly or be handled by well-controlled, plausible approximations. With few exceptions, this means systems with a small number of degrees of freedom. The exceptions are many--electron atoms, the electromagnetic field and the Dirac equation. The inclusion of the last two topics reflects the belief that every physicist should now have some knowledge of these cornerstones of modern physics. This new edition has been completely revised and rewritten throughout, but retains the clarity and readability of the first edition. Born in Vienna, Kurt Gottfried emigrated to Canada in 1939 and received his Ph.D. in theoretical physics from the Massachusetts Institute of Technology in 1955. He is a professor emeritus of physics at Cornell University, and had previously been at Harvard University and at CERN in Geneva, Switzerland. He is the coauthor of Concepts of Particle Physics (with V.F. Weisskopf) and of Crisis Stability and Nuclear War. Gottfried has done research in both nuclear and particle physics; he has an active interest in arms control and human rights and is a founder and currently the Chair of the Union of Concerned Scientists. Tung-Mow Yan, originally from Taiwan, received his Ph.D. in theoretical physics from Harvard University in 1968. He has been a member of the Cornell University faculty since 1970 after spending two years as a research associate at the Stanford Linear Accelerator Center. He has conducted research in many areas of elementary particle physics.

This text builds a solid introduction to the concepts and techniques of quantum mechanics in settings where the phenomena treated are sufficiently simple: systems that can either be solved exactly or be handled by well-controlled, plausible approximations. It includes discussions of many-electron atoms, the electromagnetic field, and the Dirac equation.
Preface vii
1 Fundamental Concepts 1(26)
1.1 Complementarity and Uncertainty
1(10)
(a) Complementarity
2(4)
(b) The Uncertainty Principle
6(5)
1.2 Superposition
11(9)
(a) The Superposition Principle
11(1)
(b) Two-Particle states
12(2)
(c) Two-Particle Interferometry
14(5)
(d) EPR Correlations
19(1)
1.3 The Discovery of Quantum Mechanics
20(4)
1.4 Problems
24(3)
2 The Formal Framework 27(86)
2.1 The Formal Language: Hilbert Space
27(12)
(a) Hilbert Space
29(1)
(b) Dirac's Notation
30(2)
(c) Operators
32(3)
(d) Unitary Transformations
35(3)
(e) Eigenvalues and Eigenvectors
38(1)
2.2 States and Probabilities
39(15)
(a) Quantum States
40(3)
(b) Measurement Outcomes
43(3)
(c) Mixtures and the Density Matrix
46(4)
(d) Entangled States
50(2)
(e) The Wigner Distribution
52(2)
2.3 Canonical Quantization
54(6)
(a) The Canonical Commutation Rules
54(2)
(b) Schrödinger Wave Functions
56(3)
(c) Uncertainty Relations
59(1)
2.4 The Equations of Motion
60(11)
(a) The Schrödinger Picture
60(5)
(b) The Heisenberg Picture
65(1)
(c) Time Development of Expectation Values
66(1)
(d) Time-Energy Uncertainty
67(3)
(e) The Interaction Picture
70(1)
2.5 Symmetries and Conservation Laws
71(13)
(a) Symmetries and Unitary Transformations
72(1)
(b) Spatial Translations
73(1)
(c) Symmetry Groups
74(2)
(d) Rotations
76(5)
(e) Space Reflection and Parity
81(1)
(f) Gauge Invariance
82(2)
2.6 Propagators and Green's Functions
84(8)
(a) Propagators
84(1)
(b) Green's Functions
85(2)
(c) The Free Particle Propagator and Green's Function
87(2)
(d) Perturbation Theory
89(3)
2.7 The Path Integral
92(6)
(a) The Feynman Path Integral
92(3)
(b) The Free-Particle Path Integral
95(3)
2.8 Semiclassical Quantum Mechanics
98(11)
(a) Hamilton-Jacobi Theory
99(3)
(b) The Semiclassical Wave Function
102(2)
(c) The Semiclassical Propagator
104(2)
(d) Derivations
106(3)
2.9 Problems
109(2)
Endnotes
111(2)
3 Basic Tools 113(52)
3.1 Angular Momentum: The Spectrum
113(3)
3.2 Orbital Angular Momentum
116(4)
3.3 Spin
120(8)
(a) Spin
121(4)
(b) Spin 1
125(2)
(c) Arbitrary Spins
127(1)
3.4 Free-Particle States
128(5)
3.5 Addition of Angular Momenta
133(9)
(a) General Results
133(2)
(b) Adding Spins and Unit Spins
135(2)
(c) Arbitrary Angular Momenta; Clebsch-Gorden Coefficients
137(3)
(d) Matrix Elements of Vector Operators
140(2)
3.6 The Two-Body Problem
142(7)
(a) Center-of-Mass and Relative Motion
142(2)
(b) The Radial Schrödinger Equation: General Case
144(3)
(c) Bound-State Coulomb Wave Functions
147(2)
3.7 Basic Approximation Methods
149(13)
(a) Stationary-State Perturbation Theory
150(3)
(b) Degenerate-State Perturbation Theory
153(3)
(c) Time-Dependent Perturbation Theory
156(3)
(d) The Golden Rule
159(2)
(e) The Variational Principle
161(1)
3.8 Problems
162(3)
4 Low-Dimensional systems 165(70)
4.1 Spectroscopy in Two-Level Systems
166(8)
(a) Level Crossings
166(3)
(b) Resonance Spectroscopy
169(5)
4.2 The Harmonic Oscillator
174(14)
(a) Equations of Motion
174(1)
(b) Energy Eigenvalues and Eigenfunctions
175(3)
(c) The Forced Oscillator
178(3)
(d) Coherent States
181(3)
(e) Wigner Distributions
184(2)
(f) Propagator and Path Integral
186(2)
4.3 Motion in a Magnetic Field
188(10)
(a) Equations of Motion and Energy Spectrum
188(2)
(b) Eigenstates of Energy and Angular Momentum
190(4)
(c) Coherent states
194(2)
(d) The Aharonov-Bohm Effect
196(2)
4.4 Scattering in One Dimension
198(18)
(a) General Properties
198(4)
(b) The Delta-Function Potential
202(2)
(c) Resonant Transmission and Reflection
204(9)
(d) The Exponential Decay Law
213(3)
4.5 The Semiclassical Approximation
216(12)
(a) The WKB Approximation
217(1)
(b) Connection Formulas
218(4)
(c) Energy Eigenvalues, Barrier Transmission, and a-Decay
222(3)
(d) Exactly Solvable Examples
225(3)
4.6 Problems
228(5)
Endnotes
233(2)
5 Hydrogenic Atoms 235(32)
5.1 Qualitative Overview
235(3)
5.2 The Kepley Problem
238(7)
(a) The Lenz Vector
238(2)
(b) The Energy Spectrum
240(2)
(c) The Conservation of M
242(1)
(d) Wave Functions
243(2)
5.3 Fine and Hyperfine Structure
245(9)
(a) Fine Structure
245(4)
(b) Hyperfine Structure - General Features
249(1)
(c) Magnetic Dipole Hfs
250(2)
(d) Electric Quadrupole Hfs
252(2)
5.4 The Zeeman and Stark Effects
254(9)
(a) Order of Magnitude Estimates
254(3)
(b) The n = 2 Multiplet
257(3)
(c) Strong Fields
260(3)
5.5 Problems
263(3)
Endnotes
266(1)
6 Two-Electron Atoms 267(16)
6.1 Two Identical Particles
267(5)
(a) Spin and Statistics
267(2)
(b) The Exclusion Principle
269(1)
(c) Symmetric and Antisymmetric States
270(2)
6.2 The Spectrum of Helium
272(3)
6.3 Atoms with Two Valence Electrons
275(4)
(a) The Shell Model and Coupling Schemes
275(1)
(b) The Configuration p2
276(3)
6.4 Problems
279(2)
Endnotes
281(2)
7 Symmetries 283(52)
7.1 Equivalent Descriptions and Wigner's Theorem
283(3)
7.2 Time Reversal
286(6)
(a) The Time Reversal Operator
287(2)
(b) Spin 0
289(1)
(c) Spin 1/2
290(2)
7.3 Galileo Transformations
292(5)
(a) Transformation of states: Galileo Invariance
292(3)
(b) Mass Differences
295(2)
7.4 The Rotation Group
297(14)
(a) The Group SO(3)
297(2)
(b) SO(3) and SU(2)
299(2)
(c) Irreducible Representations of SU(2)
301(3)
(d) D(R) in Terms of Euler Angles
304(2)
(e) The Kronecker Product
306(1)
(f) Integration over Rotations
307(4)
7.5 Some Consequences of Symmetry
311(9)
(a) Rotation of Spherical Harmonics
312(2)
(b) Helicity States
314(2)
(c) Decay Angular Distributions
316(1)
(d) Rigid-Body Motion
317(3)
7.6 Tensor Operators
320(6)
(a) Definition of Tensor Operators
320(2)
(b) The Wigner-Eckart Theorem
322(2)
(c) Racah Coefficients and 6-j Symbols
324(2)
7.7 Geometric Phases
326(5)
(a) Spin in Magnetic Field
327(2)
(b) Correction to the Adiabatic Approximation
329(2)
7.8 Problems
331(3)
Endnotes
334(1)
8 Elastic Scattering 335(68)
8.1 Consequences of Probability and Angular Momentum Conservation
335(10)
(a) Partial Waves
335(5)
(b) Hard Sphere Scattering
340(1)
(c) Time-Dependent Description and the Optical Theorem
340(5)
8.2 General Properties of Elastic Amplitudes
345(12)
(a) Integral Equations and the Scattering Amplitude
346(4)
(b) A Solvable Example
350(3)
(c) Bound-State Poles
353(1)
(d) Symmetry Properties of the Amplitude
354(2)
(e) Relations Between Laboratory and Center-of-Mass Quantities
356(1)
8.3 Approximations to Elastic Amplitudes
357(11)
(a) The Born Approximation
358(3)
(b) Validity of the Born Approximation
361(3)
(c) Short-Wavelength Approximations
364(4)
8.4 Scattering in a Coulomb Field
368(8)
(a) The Coulomb Scattering Amplitude
368(5)
(b) The Influence of a Short-Range Interaction
373(3)
8.5 Scattering of Particles with spin
376(6)
(a) Symmetry Properties
377(1)
(b) Cross Section and Spin Polarization
378(1)
(c) Scattering of a Spin 1/2 Particle by a Spin 0 Target
379(3)
8.6 Neutron-Proton Scattering and the Deuteron
382(10)
(a) Low-Energy Neutron-Proton Scattering
383(2)
(b) The Deuteron and Low-Energy np Scattering
385(3)
(c) Neutron Scattering by the Hydrogen Molecule
388(2)
(d) The Tensor Force
390(2)
8.7 Scattering of Identical Particles
392(5)
(a) Boson-Boson Scattering
392(3)
(b) Fermion-Fermion Scattering
395(2)
8.8 Problems
397(6)
9 Inelastic Collisions 403(34)
9.1 Atomic Collision Processes
403(11)
(a) Scattering Amplitudes and Cross Sections
404(3)
(b) Elastic Scattering
407(2)
(c) Inelastic Scattering
409(3)
(d) Energy Loss
412(2)
9.2 The S Matrix
414(10)
(a) Scattering by a Bound Particle
415(2)
(b) The S Matrix
417(4)
(c) Transition Rates and Cross Sections
421(3)
9.3 Inelastic Resonances
424(9)
(a) A Solvable Model
424(4)
(b) Elastic and Inelastic Cross Sections
428(5)
9.4 Problems
433(2)
Endnotes
435(2)
10 Electrodynamics 437(66)
10.1 Quantization of the Free Field
437(13)
(a) The Classical Theory
438(3)
(b) Quantization
441(2)
(c) Photons
443(5)
(d) Space Reflection and Time Reversal
448(2)
10.2 Causality and Uncertainty in Electrodynamics
450(4)
(a) Commutation Rules: Complementarity
450(2)
(b) Uncertainty Relations
452(2)
10.3 Vacuum Fluctuations
454(6)
(a) The Casimir Effect
455(3)
(b) The Lamb Shift
458(2)
10.4 Radiative Transitions
460(8)
(a) The Interaction Between Field and Sources
461(2)
(b) Transition Rates
463(3)
(c) Dipole Transitions
466(2)
10.5 Quantum Optics
468(8)
(a) The Beam splitter
468(2)
(b) Various States of the Field
470(4)
(c) Photon Coincidences
474(2)
10.6 The Photoeffect in Hydrogen
476(6)
(a) High Energies
476(2)
(b) The Cross Section Near Threshold
478(4)
10.7 Scattering of Photons
482(3)
10.8 Resonant Scattering and Spontaneous Decay
485(11)
(a) Model Hamiltonian
486(2)
(b) The Elastic Scattering Cross Section
488(4)
(c) Decay of the Excited State
492(3)
(d) The Connection Between Self-Energy and Resonance Width
495(1)
10.9 Problems
496(5)
Endnotes
501(2)
11 Systems of Identical Particles 503(36)
11.1 Indistinguishability
503(3)
11.2 Second Quantization
506(13)
(a) Bose-Einstein Statistics
507(6)
(b) Fenmi-Dirac Statistics
513(3)
(c) The Equations of Motion
516(2)
(d) Distribution Functions
518(1)
11.3 Ideal Gases
519(7)
(a) The Grand Canonical Ensemble
520(1)
(b) The Ideal Fenmi Gas
521(3)
(c) The Ideal Bose Gas
524(2)
11.4 The Mean Field Approximation
526(9)
(a) The Dilute Bose-Einstein Condensate
527(3)
(b) The Hartree-Fock Equations
530(5)
11.5 Problems
535(4)
12 Interpretation 539(38)
12.1 The Critique of Einstein, Podolsky and Rosen
540(4)
12.2 Hidden Variables
544(2)
12.3 Bell's Theorem
546(8)
(a) The Spin Singlet State
547(1)
(b) Bell's Theorem
548(2)
(c) The Clausen-Home Inequality
550(1)
(d) An Experimental Test of Bell's Inequality
551(3)
12.4 Locality
554(4)
12.5 Measurement
558(16)
(a) A Measurement Device
558(4)
(b) Coherence and Entropy Following Measurement
562(4)
(c) An Optical Analogue to the Stem-Gerlach Experiment
566(4)
(d) A Delayed Choice Experiment
570(2)
(e) Summation
572(2)
12.6 Problems
574(1)
Endnotes
575(2)
13 Relativistic Quantum Mechanics 577(30)
13.1 Introduction
577(2)
13.2 The Dirac Equation
579(10)
(a) Lorentz Transformations of Spinous
580(4)
(b) The Free-Particle Dirac Equation
584(3)
(c) Charge and Current Densities
587(2)
13.3 Electromagnetic Interaction of a Dirac Particle
589(8)
(a) The Dime Equation in the Presence of a Field
589(2)
(b) The Magnetic Moment
591(2)
(c) The Fine Structure Hamiltonian
593(2)
(d) Antiparticles and Charge Conjugation
595(2)
13.4 Scattering of Ultra-Relativistic Electrons
597(3)
13.5 Bound States in a Coulomb Field
600(5)
13.6 Problems
605(1)
Endnotes
606(1)
Appendix 607(3)
Index 610

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