| Preface |
|
vii | |
| 1 Fundamental Concepts |
|
1 | (26) |
|
1.1 Complementarity and Uncertainty |
|
|
1 | (10) |
|
|
|
2 | (4) |
|
(b) The Uncertainty Principle |
|
|
6 | (5) |
|
|
|
11 | (9) |
|
(a) The Superposition Principle |
|
|
11 | (1) |
|
|
|
12 | (2) |
|
(c) Two-Particle Interferometry |
|
|
14 | (5) |
|
|
|
19 | (1) |
|
1.3 The Discovery of Quantum Mechanics |
|
|
20 | (4) |
|
|
|
24 | (3) |
| 2 The Formal Framework |
|
27 | (86) |
|
2.1 The Formal Language: Hilbert Space |
|
|
27 | (12) |
|
|
|
29 | (1) |
|
|
|
30 | (2) |
|
|
|
32 | (3) |
|
(d) Unitary Transformations |
|
|
35 | (3) |
|
(e) Eigenvalues and Eigenvectors |
|
|
38 | (1) |
|
2.2 States and Probabilities |
|
|
39 | (15) |
|
|
|
40 | (3) |
|
|
|
43 | (3) |
|
(c) Mixtures and the Density Matrix |
|
|
46 | (4) |
|
|
|
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) |
|
|
|
73 | (1) |
|
|
|
74 | (2) |
|
|
|
76 | (5) |
|
(e) Space Reflection and Parity |
|
|
81 | (1) |
|
|
|
82 | (2) |
|
2.6 Propagators and Green's Functions |
|
|
84 | (8) |
|
|
|
84 | (1) |
|
|
|
85 | (2) |
|
(c) The Free Particle Propagator and Green's Function |
|
|
87 | (2) |
|
|
|
89 | (3) |
|
|
|
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) |
|
|
|
106 | (3) |
|
|
|
109 | (2) |
|
|
|
111 | (2) |
| 3 Basic Tools |
|
113 | (52) |
|
3.1 Angular Momentum: The Spectrum |
|
|
113 | (3) |
|
3.2 Orbital Angular Momentum |
|
|
116 | (4) |
|
|
|
120 | (8) |
|
|
|
121 | (4) |
|
|
|
125 | (2) |
|
|
|
127 | (1) |
|
|
|
128 | (5) |
|
3.5 Addition of Angular Momenta |
|
|
133 | (9) |
|
|
|
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) |
|
|
|
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) |
|
|
|
159 | (2) |
|
(e) The Variational Principle |
|
|
161 | (1) |
|
|
|
162 | (3) |
| 4 Low-Dimensional systems |
|
165 | (70) |
|
4.1 Spectroscopy in Two-Level Systems |
|
|
166 | (8) |
|
|
|
166 | (3) |
|
(b) Resonance Spectroscopy |
|
|
169 | (5) |
|
4.2 The Harmonic Oscillator |
|
|
174 | (14) |
|
|
|
174 | (1) |
|
(b) Energy Eigenvalues and Eigenfunctions |
|
|
175 | (3) |
|
(c) The Forced Oscillator |
|
|
178 | (3) |
|
|
|
181 | (3) |
|
|
|
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) |
|
|
|
194 | (2) |
|
(d) The Aharonov-Bohm Effect |
|
|
196 | (2) |
|
4.4 Scattering in One Dimension |
|
|
198 | (18) |
|
|
|
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) |
|
|
|
218 | (4) |
|
(c) Energy Eigenvalues, Barrier Transmission, and a-Decay |
|
|
222 | (3) |
|
(d) Exactly Solvable Examples |
|
|
225 | (3) |
|
|
|
228 | (5) |
|
|
|
233 | (2) |
| 5 Hydrogenic Atoms |
|
235 | (32) |
|
|
|
235 | (3) |
|
|
|
238 | (7) |
|
|
|
238 | (2) |
|
|
|
240 | (2) |
|
(c) The Conservation of M |
|
|
242 | (1) |
|
|
|
243 | (2) |
|
5.3 Fine and Hyperfine Structure |
|
|
245 | (9) |
|
|
|
245 | (4) |
|
(b) Hyperfine Structure - General Features |
|
|
249 | (1) |
|
|
|
250 | (2) |
|
(d) Electric Quadrupole Hfs |
|
|
252 | (2) |
|
5.4 The Zeeman and Stark Effects |
|
|
254 | (9) |
|
(a) Order of Magnitude Estimates |
|
|
254 | (3) |
|
|
|
257 | (3) |
|
|
|
260 | (3) |
|
|
|
263 | (3) |
|
|
|
266 | (1) |
| 6 Two-Electron Atoms |
|
267 | (16) |
|
6.1 Two Identical Particles |
|
|
267 | (5) |
|
|
|
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) |
|
|
|
276 | (3) |
|
|
|
279 | (2) |
|
|
|
281 | (2) |
| 7 Symmetries |
|
283 | (52) |
|
7.1 Equivalent Descriptions and Wigner's Theorem |
|
|
283 | (3) |
|
|
|
286 | (6) |
|
(a) The Time Reversal Operator |
|
|
287 | (2) |
|
|
|
289 | (1) |
|
|
|
290 | (2) |
|
7.3 Galileo Transformations |
|
|
292 | (5) |
|
(a) Transformation of states: Galileo Invariance |
|
|
292 | (3) |
|
|
|
295 | (2) |
|
|
|
297 | (14) |
|
|
|
297 | (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) |
|
|
|
314 | (2) |
|
(c) Decay Angular Distributions |
|
|
316 | (1) |
|
|
|
317 | (3) |
|
|
|
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) |
|
|
|
326 | (5) |
|
(a) Spin in Magnetic Field |
|
|
327 | (2) |
|
(b) Correction to the Adiabatic Approximation |
|
|
329 | (2) |
|
|
|
331 | (3) |
|
|
|
334 | (1) |
| 8 Elastic Scattering |
|
335 | (68) |
|
8.1 Consequences of Probability and Angular Momentum Conservation |
|
|
335 | (10) |
|
|
|
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) |
|
|
|
350 | (3) |
|
|
|
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) |
|
|
|
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) |
|
|
|
390 | (2) |
|
8.7 Scattering of Identical Particles |
|
|
392 | (5) |
|
(a) Boson-Boson Scattering |
|
|
392 | (3) |
|
(b) Fermion-Fermion Scattering |
|
|
395 | (2) |
|
|
|
397 | (6) |
| 9 Inelastic Collisions |
|
403 | (34) |
|
9.1 Atomic Collision Processes |
|
|
403 | (11) |
|
(a) Scattering Amplitudes and Cross Sections |
|
|
404 | (3) |
|
|
|
407 | (2) |
|
|
|
409 | (3) |
|
|
|
412 | (2) |
|
|
|
414 | (10) |
|
(a) Scattering by a Bound Particle |
|
|
415 | (2) |
|
|
|
417 | (4) |
|
(c) Transition Rates and Cross Sections |
|
|
421 | (3) |
|
|
|
424 | (9) |
|
|
|
424 | (4) |
|
(b) Elastic and Inelastic Cross Sections |
|
|
428 | (5) |
|
|
|
433 | (2) |
|
|
|
435 | (2) |
| 10 Electrodynamics |
|
437 | (66) |
|
10.1 Quantization of the Free Field |
|
|
437 | (13) |
|
|
|
438 | (3) |
|
|
|
441 | (2) |
|
|
|
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) |
|
|
|
454 | (6) |
|
|
|
455 | (3) |
|
|
|
458 | (2) |
|
10.4 Radiative Transitions |
|
|
460 | (8) |
|
(a) The Interaction Between Field and Sources |
|
|
461 | (2) |
|
|
|
463 | (3) |
|
|
|
466 | (2) |
|
|
|
468 | (8) |
|
|
|
468 | (2) |
|
(b) Various States of the Field |
|
|
470 | (4) |
|
|
|
474 | (2) |
|
10.6 The Photoeffect in Hydrogen |
|
|
476 | (6) |
|
|
|
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) |
|
|
|
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) |
|
|
|
496 | (5) |
|
|
|
501 | (2) |
| 11 Systems of Identical Particles |
|
503 | (36) |
|
11.1 Indistinguishability |
|
|
503 | (3) |
|
|
|
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) |
|
|
|
519 | (7) |
|
(a) The Grand Canonical Ensemble |
|
|
520 | (1) |
|
|
|
521 | (3) |
|
|
|
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) |
|
|
|
535 | (4) |
| 12 Interpretation |
|
539 | (38) |
|
12.1 The Critique of Einstein, Podolsky and Rosen |
|
|
540 | (4) |
|
|
|
544 | (2) |
|
|
|
546 | (8) |
|
(a) The Spin Singlet State |
|
|
547 | (1) |
|
|
|
548 | (2) |
|
(c) The Clausen-Home Inequality |
|
|
550 | (1) |
|
(d) An Experimental Test of Bell's Inequality |
|
|
551 | (3) |
|
|
|
554 | (4) |
|
|
|
558 | (16) |
|
|
|
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) |
|
|
|
572 | (2) |
|
|
|
574 | (1) |
|
|
|
575 | (2) |
| 13 Relativistic Quantum Mechanics |
|
577 | (30) |
|
|
|
577 | (2) |
|
|
|
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) |
|
|
|
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) |
|
|
|
605 | (1) |
|
|
|
606 | (1) |
| Appendix |
|
607 | (3) |
| Index |
|
610 | |