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Quantum Theory

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Quantum Theory

ویرایش: 1st. Edition, 10th Printing 
نویسندگان:   
سری: Prentice-Hall Physics Series 
 
ناشر: Prentice-Hall, Inc. 
سال نشر: 1951 
تعداد صفحات: 660 
زبان: English 
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود) 
حجم فایل: 14 مگابایت 

قیمت کتاب (تومان) : 41,000



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فهرست مطالب

Quantum Theory......Page 1
Title-Page......Page 3
Copyright......Page 4
PREFACE......Page 5
CONTENTS......Page 9
PART I - PHYSICAL FORMULATION OF THE QUANTUM THEORY......Page 13
1. Blackbody Radiation in Equilibrium......Page 17
3. Electromagnetic Potentials......Page 19
4. Boundary Conditions......Page 21
5. Fourier Analysis......Page 22
6. Polarization of Waves......Page 24
7. Evaluation of the Electromagnetic Energy......Page 25
8. Meaning of Preceding Result for Electromagnetic Energy......Page 26
9. Number of Oscillators......Page 27
10. Equipartition of Energy......Page 28
11. The Quantization of the Radiation Oscillators......Page 30
13. Material vs. Radiation Oscillators......Page 31
14. Quantization of Material Oscillators......Page 32
15. Summary......Page 34
1. Photoelectric Effect......Page 35
3. The Indivisibility of Quantum Processes......Page 38
4. Probability and Incomplete Determinism in Quantum Laws......Page 39
5. Unlikelihood of Completely Deterministic Laws on a Deeper Level......Page 41
6. Correspondence Principle......Page 42
7. Particle Properties of Light......Page 43
8. Compton Effect. The Scattering of Electromagnetic Radiation......Page 45
9. Analysis of the Compton Effect......Page 46
The Quantization of Material Systems......Page 49
10. Evidence for Quantization of All Material Systems......Page 50
11. Determination of Energy Levels......Page 51
13. Quantization of Angular Momentum......Page 53
14. The Hydrogen Atom......Page 54
Correspondence Theory of Radiation......Page 60
16. Absorption of Radiation......Page 61
17. Emission of Radiation......Page 66
Summary.......Page 70
1. Introduction......Page 71
2. Motion of Pulses of Light......Page 72
3. The Width of a Wave Packet......Page 74
4. Group Velocity......Page 75
5. Spread of Wave Packets......Page 77
7. Generalization to Three Dimensions......Page 79
8. Motion of Electron Wave Packets......Page 80
9. Effects of Forces......Page 81
10. Effects of Quantization......Page 82
12. Prediction of Electron Diffraction by Bohr-Sommerfeld Theory......Page 83
13. Interpretation of Wave Function in Terms of Probability......Page 85
14. Comparison between Electron Waves and Electromagnetic Waves......Page 86
15. More Detailed Picture of Electron Waves......Page 87
16. Transitions between Orbits......Page 88
17. Fourier Analysis. Fourier Integrals......Page 89
18. Wave Propagation for Free Particle.......Page 90
19. Wave Equation for Free Particle......Page 91
2. Choice of Probability Function P(x)......Page 93
3. Proof of Conservation of Probability......Page 94
4. Probability Current......Page 95
5. Is the Above Formulation the Most General One?......Page 96
6. Relativistic Theories......Page 101
7. The Probability Function for Light Quanta......Page 103
8. Probability of a Given Momentum......Page 104
9. The Relation between P(x) and P(k)......Page 107
10. Normalization Coefficient for P(k)......Page 108
Summary on Probabilities......Page 109
2. Proof of Uncertainty Principle for Electrons......Page 111
3. On the Interpretation of the Uncertainty Principle......Page 112
5. Relation of Stability of Atoms to Uncertainty Principle......Page 113
7. Modification of Measurements by Quantum Effects......Page 115
8. Microscope......Page 116
9. Measurement of Momentum......Page 117
11. Uncertainty Principle Applied to Light Quanta......Page 119
12. Observation of Light Quanta with Electron Microscope......Page 120
13. Localization of Electromagnetic Energy and Momentum by Means of Slits and Shutters......Page 123
14. Application of Uncertainty Principle to Problem of Defining Orbits in Atoms......Page 124
15. More General Application of Uncertainty Principle......Page 125
17. Are there Hidden Variables Underlying the Quantum Theory?......Page 126
1. The Interference Pattern, and the Wave-particle Nature of Matter......Page 128
2. Impossibility of Simultaneous Observation of Wave and Particle Properties of Matter......Page 130
3. Effects of Process of Observation on the Wave Function......Page 132
4. Relationship of Destruction of Interference to Consistency of Wave-particle Duality......Page 136
5. Generalization of Previous Results......Page 139
6. Measurement of Momentum......Page 141
8. Importance of Phase Relations......Page 143
9. Quantwn Properties of Matter as Potentialities......Page 144
11. On the Reality of the Wave Properties of Matter......Page 145
12. Wave-mechanical Interpretation of a Track in a Cloud Chamber......Page 149
13. Qualitative Picture of the Quantum Properties of Matter......Page 150
CHAPTER 7 - Summary of Quantum Concepts Introduced......Page 153
1. The Need for New Concepts......Page 156
3. Simple and Pictorial Ideas about Continuity of Motion......Page 157
5. Similarity of Simple Ideas about Fixed Position and Quantum Concepts......Page 158
6. More Sophisticated Ideas, Including Concept of Continuous Trajectory......Page 159
8. Early Ideas on Cause and Effect......Page 160
9. Completely Deterministic vs. Causal Laws as Tendencies......Page 162
10. Classical Theory Prescriptive and not Causal......Page 163
11. New Properties of Quantum Concepts: Approximate and Statistical Causality......Page 164
12. Energy and Momentum in Classical and Quantum Theories......Page 165
13. Momentum and Energy a Description of Causal Aspects of Matter......Page 167
14. Relation between Space Time and Causal Aspects of Matter......Page 168
15. The Principle of Complementarity......Page 170
16. The Indivisible Unity of the World......Page 173
17. Distinction between Object and Environment on Classical Level......Page 174
19. The Role of Causal Laws......Page 175
20. Analysis and Synthesis......Page 176
23. An Attempt to Analyze a Quantum System into Parts......Page 177
25. An Example: the Hydrogen Atom......Page 178
Summary of New Concepts in Quantum Theory......Page 179
Analogies to Ouantum Processes......Page 180
27. The Uncertainty Principle and Certain Aspects of Our Thought Processes......Page 181
28. Possible Reason for Analogies between Thought and Quantum Processes......Page 182
1. Wave Formalism and Probability......Page 185
2. Hypothesis of Linear Superposition......Page 186
3. Concept of the State of a System in Quantum Theory......Page 187
4.. Statistical Significance of the Concept of Quantum State......Page 188
Avarege Value of a Function of Position......Page 189
Criterion For Acceptable Wave Functions......Page 190
6. Operator Notation to Obtain Momentum Averages from Integrals in Position Space......Page 191
7. Functions of the Momentum......Page 192
8. Operators in Momentum Space. The Momentum Representation......Page 193
12. General Functions Expressed as Operators......Page 194
13. Reality of Average Values and the Order of Factors......Page 195
14. Hermitean Operators......Page 196
15. Modified Rule for Average of f(x, p)......Page 197
16. Hermitean Conjugate Operators......Page 198
17. Generalized Definition of a Hermitean Operator......Page 200
18. Generalized Definition of Hermitean Conjugates......Page 201
20. Application to Commutators......Page 202
22. General Form of Schrodinger's Equation......Page 203
24. Determination of H from Correspondence Principle......Page 204
25. General Formula for Time Derivative of Average Value of a Variable......Page 205
26. Application to Evaluation of Average Motion of Wave Packet......Page 206
29. Significance of Wave Equation......Page 208
32. Conservation of Energy......Page 209
2. Extension to Quantum Theory......Page 211
3. Correlations between p and x......Page 212
5. Specification of a Classical Statistical System through Mean Values of x^n p^m......Page 213
7. Application to Spreading Wave Packet for a Free Particle......Page 214
8. Semi-classical Picture of Particle with Uncertain Position and Momentum......Page 215
9. A Generalization of the Uncertainty Principle......Page 217
10. The Unusual Properties of the Gaussian Wave Function......Page 219
11. The Many-particle Problem......Page 220
12. Eigenvalues and Eigenfunctions of Operators......Page 221
13. Examples of Eigenfunctions and Eigenvalues in Position Space......Page 222
14. Degenerate Operators......Page 223
15. The Dirac Delta Function......Page 224
17. Momentum Representation of Eigenfunctions of x......Page 226
18. Connection Between Eigenfunctions of x in Position Space and in Momentum Space......Page 227
19. Differentiation of the Delta Function......Page 228
21. The Expansion of an Arbitrary Function as a Series of Eigenfunctions......Page 229
24. The Orthogonality of Eigenfunctions of a Hermitean Operator......Page 231
26. Expansion of Dirac Delta Function in Terms of Eigenfunctions of an Arbitrary Hermitean Operator......Page 232
27. Representation of an Operator in Terms of Its Eigenfunctions......Page 233
28. Mean Value of f(A) in Terms of Expansion into Eigenfunction of A......Page 234
30. Interference of Probabilities......Page 235
33. Change of Probability with Time. Stationary States......Page 237
34. Relation of Time-dependent Probabilities to Uncertainty Principle......Page 238
36. Change of Probability with Time for a General Wave Function......Page 239
1. Introduction to Part III......Page 241
3. Square Potentials......Page 242
4. Solution of Problem of Square Potential......Page 244
5. Penetration of a Barrier......Page 250
6. Applications of Barrier Penetration......Page 252
7. The Square Well Potential......Page 254
8. Width of Peak in Transmission Resonances......Page 257
9. The Ramsauer Effect......Page 258
10. Bound States......Page 259
11. Limit of an Infinitely Deep Well......Page 263
12. Graphical Interpretation of Solutions......Page 264
13. Application of Expansion Theorem......Page 265
14. Application to Deuteron......Page 266
16. Use of Observed Energy Levels to Provide Information about the Potential......Page 268
17. Wave Packets Made up from Eigenfunctions in the Continuum......Page 269
19. Time Delay of Wave as It Crosses Potential Well......Page 272
20. Metastable (or Virtual) States of Trapping an Object within a Well......Page 273
21. Metastable Singlet State of Deuteron......Page 274
1. Introduction......Page 276
2. The WKB Approximation......Page 277
4. Physical Interpretation of Solutions in Terms of Classical Distribution of Particles......Page 280
6. Wave Packets. The Time-dependent Solution......Page 281
6. Time-dependent Three-dimensional WKB Approximation......Page 282
8. Connection Formulas......Page 283
9. Connection Formulas......Page 285
10. Probability of Penetration of a Barrier......Page 287
11. Applications of Barrier Penetration Probability......Page 289
12. Probability of Penetration into Nucleus from Outside......Page 292
13. Bound States of a Potential Well......Page 293
14:. Virtual or Metastable States in the WKB Approximation......Page 295
15. Discussion of Eq. (64) for Transmissivity......Page 298
16. Width of Resonance. Transmission Coefficient near Resonance......Page 299
17. Intensity of Wave Inside Well......Page 300
18. Formation of Wave Packets. Lifetimes of Virtual States......Page 302
19. Wave Packet Inside Well (near Resonance)......Page 303
21. Application to Radioactive Systems......Page 305
22. Application to Nuclear Reactions......Page 306
2. Wave Equation......Page 308
3. General Form of Solutions......Page 309
6. Schrodinger's Method of Factorization......Page 310
6. Solution for Wave Functions......Page 312
7. Hermite Polynomials......Page 313
8. Normalization Factor......Page 314
10. Recurrence Relations......Page 315
12. General Form of Solution......Page 316
14. Expansion Postulate......Page 317
15. Wave Packets......Page 318
16. Mean Values of Kinetic and Potential Energies......Page 320
1. Separation of Variables......Page 322
2. Angular Momentum......Page 323
3. Commutation Rules for Angular Momentum......Page 324
5. Angular Momentum in Polar Co-ordinates......Page 325
7. Eigenvalues of Lz......Page 326
10. Determination of Simultaneous Eigenvalues and Eigenfunctions of Lz and L^2......Page 327
12. Effect of Fluctuation in Direction of L......Page 330
13. Eigenfunctions of L^2 and Lz......Page 331
14. Legendre Polynomials......Page 333
15. Associated Legendre Functions......Page 335
16. Measurement of Angular Momentum. Stern-Gerlach Experiment......Page 338
17. Transformation to a Rotated System of Axes......Page 339
19. Physical Equivalence of All Co-ordinate Systems......Page 342
21. Application to Construction of Orbits......Page 344
1. The Radial Equation......Page 346
4. Centrifugal Potential......Page 347
5. Separation into Relative Co-ordinates......Page 348
7. General Form of Solution for s Waves......Page 350
8. General Form of Solution When l > 0......Page 354
10. Physical Interpretation of Wave Functions of Different n, l, m......Page 355
12. Exact Solution for Hydrogen Atom......Page 357
13. Degeneracy of Hydrogen Energy Levels......Page 360
14. The Laguerre Polynomials and the Associated Laguerre Polynomials......Page 361
15. Three-dimensional Harmonic Oscillator......Page 363
19. An Important Property of Degenerate Eigenfunctions......Page 365
20. Relation of Hermite Polynomials to Spherical Harmonics......Page 366
21. The Hamiltonian for a Charged Particle in a Given Electromagnetic Field......Page 367
22. Quantum-mechanical Hamiltonian......Page 368
25. Gauge Invariance......Page 369
27. The Zeeman Splitting of Levels of Different m......Page 371
1. Matrix Representation of an Operator......Page 373
2. Properties of Matrices......Page 374
4. An Example: Harmonic-oscillator Wave Functions......Page 377
7. Commutation of Diagonal Matrices......Page 378
8. Continuous Matrices......Page 379
9. Column Representation of the Wave Function......Page 380
10. Normalization and Orthogonality of Wave Functions in Column Representation......Page 381
12. Eigenvalues and Eigenvectors of Matrices......Page 382
13. Change of Representation......Page 383
15. Significance of the Unitary Transformation......Page 384
17. Simultaneous Eigenfunctions of Commuting Operators......Page 387
18. The Specification of an Arbitrary Operator in Terms of Its Commutators with a Complete Commuting Set of Operators......Page 389
19. Schrodinger's Equation in an Arbitrary Representation......Page 390
21. The Heisenberg Representation......Page 391
22. Time Rate of Change of Operators in a Heisenberg Representation......Page 392
23. Poisson Brackets......Page 394
24. Heisenberg's Formulation of Quantum Theory......Page 395
25. Physical Interpretation of Matrix Representations and Transformation Theory......Page 396
1. Electron Spin......Page 399
2. Matrix Representation of Angular-momentum Operators......Page 400
3. The Allowed Values of l and m; Half-integral Angular-momentum Quantum Numbers......Page 401
4. Matrices for (Lx + i Ly) and (Lx - i Ly)......Page 402
5. The Eigenfunctions of the sigma Operators......Page 404
7. Spinor Transformations......Page 405
8. The Addition of Angular Momenta......Page 409
9. Addition of Spin Angular Momenta of Two Separate Particles......Page 410
10. Probability Distribution of Spin States in a Statistical Ensemble......Page 412
11. Addition of Orbital and Spin Angular Momenta of a Given Particle......Page 413
12. Discussion of General Problem of Adding Angular Momenta......Page 416
13. Energy of a Spinning Electron......Page 417
2. Case of a Small Perturbation (Method of Variation of Constants)......Page 419
4. Methods of Approximation......Page 422
5. Interpretation of the |Cm|^2 in Terms of Transition Probabilities......Page 423
7. Case a: Vmn Turned on Suddenly (Calculation to First Order in lambda)......Page 424
9. A Description of Transitions in Terms of Quantum Fluctuations......Page 425
10. Microscopic Reversibility of Transition Processes......Page 427
11. Conservation of Probability......Page 428
12. Case b: Trigonometric Variation of Vmn with Time, with Application to Absorption and Emission of Light......Page 429
14. Interpretation of Results......Page 430
15. Present Treatment Does Not Quantize Radiation Field......Page 431
17. Relation between Vector Potential and Intensity......Page 432
18. Effect of Distribution of Frequencies of the Incident Light Wave......Page 433
20. Induced Emission of Quanta......Page 435
23. Einstein's Treatment of Spontaneous Emission......Page 436
24. Applications of Transition Theory......Page 438
25. Electric Dipole Approximation......Page 439
26. Evaluation of alpha_nm for Isotropic Harmonic Oscillator......Page 441
27. Selection Rules for Harmonic Oscillator......Page 442
29. Introduction of Parity......Page 443
30. Selection Rules on Parity......Page 444
31. Selection Rules for Spherically Symmetric Potential, with the Neglect of Spin......Page 445
32. Forbidden Transitions, Electric Quadripole Radiation......Page 447
34. Selection Rules for Electric Quadripole Radiation......Page 448
36. Higher Order Transitions......Page 449
38. Total Rate of Radiation......Page 450
39. Comparison with Classical Theory......Page 451
41. Circular Polarization......Page 453
43. Quantum Treatment......Page 454
45. Application to Normal Zeeman Effect......Page 455
46. Quantum Description of Normal Zeeman Effect......Page 457
49. Effects of Electron Spin on Transition Probabilities......Page 458
50. Case c: Vmn Varies Slowly with the Time (Adiabatic Case).......Page 460
51. Adiabatic Turning on of Potential Results in Perturbed Stationary......Page 462
52. Perturbation of Stationary-state Wave Functions......Page 465
53. Interpretation of Second-order Fonnulas for Energy......Page 468
54. Application of Perturbation Theory......Page 470
1. Introduction......Page 474
2. Example: Doubly Degenerate Level......Page 475
5. Higher Approximations......Page 476
6. More Than Two Degenerate Levels......Page 477
8. Time-dependent Solution for Special Case of Two Degenerate Levels......Page 478
9. Quantum-mechanical "Resonance"......Page 479
10. Analogy of Degeneracy Problem to Principal Axis Transformation......Page 481
11. First-order Stark Effect......Page 482
12. Classical Interpretation of Linear Stark Etlect......Page 483
13. Van der Waals Forces between Atoms......Page 484
14. Quantum-mechanical Analogue of Oscillator Phase......Page 490
16. Experimental Consequences of Degeneracy......Page 491
16. Exchange Degeneracy......Page 492
17. Solution of Problem......Page 493
19. Evaluation of the Energy......Page 494
20. Higher Approximations......Page 497
21. Effects of Spin......Page 498
23. Correlation between Exchange Energy and Electron Spin Brought about by Antisymmetry of Wave Functions......Page 500
25. A System of Many Electrons......Page 502
26. Pauli Exclusion Principle......Page 503
28. Totally Symmetric Wave Functions......Page 504
29. Indistinguishability of Equivalent Particles......Page 505
1. General Adiabatic Perturbations......Page 508
2. Interpretation of Results......Page 512
3. Applications......Page 513
4. The Approximation of Sudden Change of Potential......Page 519
5. Application. Emission of Electron from Nucleus in Beta-Decay......Page 520
6. Relation between Perturbation Theory and Theory of Sudden Transitions......Page 521
2. Classical Theory of Scattering......Page 523
3. Definition of Cross Section......Page 524
5. Cross Section as a Function of Scattering Angle......Page 525
6. Difierential Cross Sections......Page 526
7. More General Theory of Scattering......Page 528
8. The Approximation of Small Deflections. Classical Perturbation Theory......Page 529
9. Cross Section for Energy and Momentum Transfer......Page 532
10. Exact Solution for Scattering......Page 533
11. Use of Cross Sections to Investigate Law of Force......Page 535
12. Transformation from Center-of-Mass System to Laboratory System of Co-ordinates......Page 536
15. Quantum Theory of Scattering......Page 539
16. Condition for Validity of Classical Theory of Scattering......Page 540
17. Quantum Description of Scattering......Page 541
18. Scattering Considered as a Transition between Different States in Momentum Space......Page 543
19. Born Approximation. Perturbation Theory......Page 545
20. Evaluation of Cross Section......Page 548
21. Example of Application: The Shielded Coulomb Force......Page 549
22. Relation between Born Approximation and Fourier Analysis of the Potential......Page 550
23. Illustration: Comparison of Cross Sections for Gaussian Potential and Square Well......Page 551
24. The Space-time Representation of Scattering......Page 553
25. New Form for Schrodinger's Equation......Page 555
26. Interpretation of Results......Page 558
28. Relation of Space-time and Causal Descriptions......Page 559
29. Relation of Stationary-state Method to Time Dependent Descriptions......Page 560
30. Another Application of the Bom Approximation: Scattering from a Crystal Lattice......Page 562
31. Conditions for Validity of Born Approximation......Page 563
32. Application to Screened Coulomb Scattering......Page 564
33. Another Criterion for Validity of Born Approximation......Page 565
36. Unusual Properties of Coulomb Force......Page 566
37. Lack of Applicability of Born Approximation to Nuclei......Page 567
38. Application to Shielded Coulomb Force......Page 568
39. Method of Partial Waves. (Rayleigh, Faxen and Holtsmark)......Page 569
41. Special Case: Coulomb Potential......Page 570
44. Interpretation of Partial Waves......Page 572
45. Boundary Conditions on Partial Waves for Free Particle......Page 573
46. Imposition of Boundary Conditions When a Potential is Present......Page 575
47. Formula for Scattering Cross Section......Page 576
48. Total Cross Section......Page 577
49. Calculation of Phase for Impenetrable Sphere......Page 578
50. Application of Enct Method to Scattering from Square Well for s Waves......Page 579
51. Ramsauer Effect......Page 580
53. Application to Nuclear Scattering......Page 582
54. Approximate Expression of Low-energy Cross Section in Terms of Binding Energy of Deuteron......Page 583
55. Spin-dependent Forces......Page 584
56. Solution for Depth of Single Well......Page 586
57. Comparison with Experiment; Measurements of Radius of Potential......Page 587
58. Coulomb Scattering......Page 589
59. Interpretation of Above Result......Page 590
60. Exchange Effects in Coulomb Scattering......Page 591
2. The Nature of the Observing Apparatus......Page 595
3. The Classical Stages of an Observing Apparatus......Page 596
4. Extent of Arbitrariness in Distinction Between the Observer and What He Sees......Page 598
5. Mathematical Treatment of Process of Observation......Page 600
6. An Example: The Measurement of the Spin of an Atom......Page 605
7. Generalization to a Variable with an Arbitrarily Large Number of Eigenvalues......Page 610
8. Destruction of Interference in the Process of Measurement......Page 612
10. Interpretation of Combined Wave Function in Terms of a Statistical Ensemble of Wave Functions for the Spin Alone......Page 614
11. Inclusion of Apparatus Co-ordinates......Page 616
12. Irreversibility of Process of Measurement and Its Fundamental Role in Quantum Theory......Page 620
13. Wave vs. Particle Properties of Matter as Potentialities......Page 621
14. On the Relation between Continuity and Discontinuity in Quantum Transfers......Page 622
15. The Paradox of Einstein, Rosen, and Podolsky......Page 623
16. The Hypothetical Experiment of Einstein, Rosen, and Podolsky......Page 626
17. Mathematical Analysis of Experiment According to Quantum Theory......Page 627
18. Physical Description of Origin of Correlations......Page 631
19. Proof that Quantum Theory Is Inconsistent with Hidden Variables......Page 634
CHAPTER 23 - Relationship between Quantum and Classical Concepts......Page 636
INDEX......Page 641
Back Cover......Page 660




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