Principles of Quantum MechanicsPDF电子书下载

Chapter Ⅰ．Foundations of Quantum Theory 1

1．Energy and Momentum of Light Quanta 1

2．Experimental Verification of the Conservation Laws for the Energy and Momentum of Light Quanta 4

3．Elementary Particles 8

4．The Bohr Theory 15

5．Elementary Quantum Theory of Radiation 18

6．Black-Body Radiation 22

7．De Broglie Waves．Group Velocity 24

8．Particle Diffraction 29

Chapter Ⅱ．Foundations of Quantum Mechanics 36

9．Statistical Interpretation of De Broglie Waves 36

10．Position Probability of a Particle 39

11．The Principle of Superposition of States 41

12．Momentum Probability of a Particle 43

13．Mean Values of Functions of the Position and Functions of the Momentum 46

14．Statistical Ensembles in Quantum Mechanics 48

15．The Uncertainty Principle 51

16．Illustrations of the Uncertainty Principle 57

17．The Role of the Measuring Apparatus 65

Chapter Ⅲ．Representation of Dynamical Variables by Operators 71

18．Linear Self-Adjoint Operators 71

19．General Expressions for the Mean and the Variance of a Variable 75

20．Eigenvalues and Eigenfunctions of Operators and Their Physical Meaning．＂Quantization＂ 77

21．Properties of Eigenfunctions 80

22．General Method of Calculating the Probability of the Result of a Measurement 84

23．Restrictions on Simultaneous Measurements of Different Dynamical Variables 87

24．Position and Momentum Operators 89

25．The Angular-Momentum Operator 91

26．The Energy Operator and the Hamiltonian 96

27．The Hamiltonian 98

Chapter Ⅳ．Time Dependence of a State 102

28．The Schrodinger Equation 102

29．Conservation of the Number of Particles 107

30．Stationary States 111

Chapter Ⅴ．Time Variation of Dynamical Variables 114

31．Time Derivatives of Operators 114

32．The Equations of Motion in Quantum Mechanics．Ehrenfest＇s Theorems 116

33．Constants of the Motion 119

Chapter Ⅵ．The Relationship of Quantum Mechanics to Classical Mechanics and Optics 122

34．Passage from Quantum-Mechanical Equations to Newton＇s Equation of Motion 122

35．Passage from the Time-Dependent Schrodinger Equation to the Classical Hamilton-Jacobi Equation 128

36．Quantum Mechanics and Optics 131

37．The Quasi-Classical Approximation(Wentzel-Kramers-Brillouin Method) 135

Chapter Ⅶ．Principles of Representation Theory 139

38．Representations of the State of a Quantum System 139

39．Operators in Different Representations．Matrices 141

40．Matrices and Matrix Operators 144

41．The Mean Value and Spectrum of a Dynamical Variable Represented by an Operator in Matrix Form 149

42．The Schrodinger Equation and the Time Dependence of Operators in Matrix Form 152

43．Unitary Transformations 156

44．Unitary Transformations Between Different Instants of Time 159

45．The Density Matrix 161

Chapter Ⅷ．The Motion of Particles in a Conservative Field of Force 166

46．Introductory Remarks 166

47．The Harmonic Oscillator 167

48．The Oscillator in the Energy Representation 174

49．Motion in a Central Field of Force 177

50．Motion in a Coulomb Field 184

51．The Energy Spectrum and Wave Functions of the Hydrogen Atom 190

52．Motion of an Electron in a Monovalent Atom 199

53．Currents in Atoms．The Magneton 203

54．Quantum Levels of a Diatomic Molecule 206

55．Motion of an Electron in a Periodic Field 214

Chapter Ⅸ．Charged Particle Motion in an Electromagnetic Field 224

56．An Arbitrary Electromagnetic Field 224

57．Motion of a Charged Particle in a Homogeneous Magnetic Field 229

Chapter Ⅹ．Intrinsic Angular Momentum and Magnetic Moment of the Electron(Spin) 233

58．Experimental Evidence for the Existence of the Spin of the Electron 233

59．The Electron Spin Operator 236

60．Spin Functions 240

61．The Pauli Equation 243

62．The Splitting of Spectral Lines in a Magnetic Field 246

63．Motion of a Particle with Spin in a Varying Magnetic Field 251

64．The Properties of the Resultant Angular Momentum 254

65．Numbering of Terms with Allowance for Spin．Multiplet Structure of Spectra 259

Chapter Ⅺ．Perturbation Theory 265

66．Formulation of the Problem 265

67．Perturbation In the Absence of Degeneracy 268

68．Perturbation in the Presence of Degeneracy 272

69．Level-Splitting in the Case of Twofold Degeneracy 277

70．Further Remarks on the Removal of Degeneracy 281

Chapter Ⅻ．Simple Applications of Perturbation Theory 284

71．The Anharmonic Oscillator 284

72．Spectral-Line Splitting in an Electric Field 286

73．Splitting of Hydrogen Lines in an Electric Field 291

74．The Splitting of Spectral Lines in a Weak Magnetic Field 295

75．The Vector Model(Splitting in a Weak Magnetic Field) 300

76．Perturbation Theory for the Continous Spectrum 302

Chapter ⅩⅢ．Scattering Theory 309

77．Formulation of the Problem 309

78．The Born Approximation 314

79．Elastic Scattering of Fast Particles by Atoms 319

80．Rigorous Scattering Theory．Phase-Shift Analysis and Effective Cross Section 327

81．The General Case 332

82．Coulomb Scattering of Charged Particles 337

Chapter ⅩⅣ．Theory of Quantum Transitions 340

83．Formulation of the Problem 340

84．The Probability of Transition Under a Time-Dependent Perturbation 343

85．Transitions Under Time-Independent Perturbations 348

Chapter ⅩⅤ．Emission，Absorption，and Scattering of Light by Atomic Systems 350

86．Introduction 350

87．Absorption and Emission of Radiation 352

88．Emission and Absorption Coefficients 356

89．The Correspondence Principle 360

90．Selection Rules for Dipole Emission 363

91．Intensities in the Emission Spectrum 368

92．Dispersion 368

93．Combination(Raman)Scattering 376

94．The Effect of the Finite Size of the Atom．Quadrupole Radiation 379

95．Photoelectric Effect 383

Chapter ⅩⅥ．Particle Transmission Through Potential Barriers 393

96．Formulation of the Problem and Simple Examples 393

97．The Tunnel Effect＂Paradox＂ 399

98．Cold Emission 401

99．Three-Dimensional Potential Barrier．Quasi-Stationary States 403

100．Theory of α-Particle Decay 410

101．Ionization of Atoms in Strong Electric Fields 414

Chapter ⅩⅦ．The Many-Body Problem 417

102．General Remarks 417

103．Conservation of the Total Momentum of a System of Particles 421

104．The Motion of the Center of Mass of a System of Particles 423

105．The Conservation of Angular Momentum 426

106．Eigenfunctions of the Angular Momentum Operator for a System of Particles．The Clebsch-Gordan Coefficients 433

107．Relation Between the Conservation Laws and the Symmetry of Space and Time 436

Chapter ⅩⅧ．Simple Applications of the Theory of Motion of Systems of Particles 441

108．The Effect of the Motion of the Nucleons in an Atom 441

109．A System of Particles Executing Small Oscillations 444

110．Motion of Atoms in an External Field 448

111．Determination of the Energy of Stationary States of Atoms by Deflection in External Fields 451

112．Inelastic Collisions of Electrons with Atoms．Determination of the Energy of the Stationary States of Atoms by the Collision Method 456

113．The Law of Conservation of Energy and the Special Role of Time in Quantum Mechanics 462

Chapter ⅩⅨ．Systems of Identical Particles 465

114．The Principle of Identity of Elementary Particles 465

115．Symmetric and Antisymmetric States 470

116．Bose and Fermi Particles．Pauli＇s Principle 472

117．Wave Functions for a System of Fermions and Bosons 479

Chapter ⅩⅩ．Second Quantization and Quantum Statistics 483

118．Second Quantization 483

119．Theory of Quantum Transitions and the Method of Second Quantization 491

120．Collision Hypothesis．Fermi-Dirac and Bose-Einstein Gases 493

Chapter ⅩⅪ．Many-Electron Atoms 501

121．Helium Atom 501

122．Approximate Quantitative Theory of the Helium Atom 509

123．Exchange Energy 514

124．The Periodic Table 518

Chapter ⅩⅫ．The Structure of Molecules 529

125．The Hydrogen Molecule 529

126．The Nature of Chemical Forces 540

127．Intermolecular Dispersive Forces 544

128．The Role of the Nuclear Spin in Diatomic Molecules 547

Chapter ⅩⅩⅢ．Magnetic Phenomena 549

129．Paramagnetism and Diamagnetism of Atoms 549

130．Ferromagnetism 552

Chapter ⅩⅩⅣ．The Atomic Nucleus 557

131．Nuclear Forces．Isotopic Spin 557

132．Classification of the States of a System of Nucleons 560

133．The Theory of the Deuteron 562

134．Nucleon-Nucleon Scattering 564

135．Polarization 569

136．Application of Quantum Mechanics 572

Appendix Ⅰ．The Fourier Transformation 575

Appendix Ⅱ．Eigenfunctions in the Case of Degeneracy 578

Appendix Ⅲ．Orthogonality and Normalization of Continuous-Spectrum Eigenfunctions．The δ-Function 580

Appendix Ⅳ．Significance of the Commutation Property of Operators 584

Appendix Ⅴ．The Spherical Harmonics 586

Appendix Ⅵ．Hamilton＇s Equation 590

Appendix Ⅶ．The Schrodinger Equation and the Equations of Motion in Terms of Curvilinear Coordinates 594

Appendix Ⅷ．Conditions Imposed on the Wave Functions 598

Appendix Ⅸ Solution of the Equation for the Harmonic Oscillator 601

Appendix Ⅹ．Electron in a Uniform Magnetic Field 606

Appendix Ⅺ．Jacobi＇s Coordinates 608

Problems 611