| Physical Constants |
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xxiii | |
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1 | (16) |
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The Franck and Hertz Experiment |
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3 | (2) |
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Interference of Matter Waves |
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5 | (5) |
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The Young Double-Slit Experiment |
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6 | (1) |
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Interference of Atoms in a Double-Slit Experiment |
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7 | (1) |
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Probabilistic Aspect of Quantum Interference |
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8 | (2) |
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The Experiment of Davisson and Germer |
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10 | (5) |
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Diffraction of X Rays by a Crystal |
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10 | (2) |
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12 | (3) |
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Summary of a Few Important Ideas |
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15 | (2) |
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15 | (1) |
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16 | (1) |
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The Wave Function and the Schrodinger Equation |
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17 | (22) |
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18 | (2) |
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Description of the State of Particle |
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18 | (1) |
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Position Measurement of the Particle |
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19 | (1) |
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Interference and the Superposition Principle |
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20 | (4) |
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20 | (1) |
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The Superposition Principle |
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21 | (1) |
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The Wave Equation in Vacuum |
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22 | (2) |
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24 | (4) |
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Definition of a Wave Packet |
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24 | (1) |
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24 | (1) |
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Structure of the Wave Packet |
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25 | (1) |
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Propagation of a Wave Packet: the Group Velocity |
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26 | (1) |
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Propagation of a Wave Packet: Average Position and Spreading |
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27 | (1) |
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Momentum Measurements and Uncertainty Relations |
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28 | (3) |
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The Momentum Probability Distribution |
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29 | (1) |
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Heisenberg Uncertainty Equations |
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30 | (1) |
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31 | (3) |
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32 | (1) |
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Particle in a Potential: Uncertainty Relations |
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32 | (1) |
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33 | (1) |
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Momentum Measurement in a Time-of-Flight Experiment |
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34 | (5) |
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36 | (1) |
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37 | (2) |
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Physical Quantities and Measurements |
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39 | (24) |
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Measurements in Quantum Mechanics |
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40 | (2) |
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The Measurement Procedure |
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40 | (1) |
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41 | (1) |
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Reinterpretation of Position and Momentum Measurements |
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41 | (1) |
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Physical Quantities and Observables |
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42 | (3) |
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Expectation Value of a Physical Quantity |
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42 | (1) |
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Position and Momentum Observables |
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43 | (1) |
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Other Observables: the Correspondence Principle |
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44 | (1) |
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Commutation of Observables |
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44 | (1) |
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Possible Results of a Measurement |
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45 | (3) |
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Eigenfunctions and Eigenvalues of an Observable |
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45 | (1) |
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Results of a Measurement and Reduction of the Wave Packet |
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46 | (1) |
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Individual Versus Multiple Measurements |
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47 | (1) |
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Relation to Heisenberg Uncertainty Relations |
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47 | (1) |
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Measurement and Coherence of Quantum Mechanics |
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48 | (1) |
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Energy Eigenfunctions and Stationary States |
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48 | (2) |
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Isolated Systems: Stationary States |
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49 | (1) |
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Energy Eigenstates and Time Evolution |
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50 | (1) |
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50 | (2) |
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Crossing Potential Barriers |
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52 | (5) |
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The Eigenstates of the Hamiltonian |
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52 | (1) |
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Boundary Conditions at the Discontinuities of the Potential |
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53 | (1) |
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Reflection and Transmission on a Potential Step |
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54 | (2) |
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Potential Barrier and Tunnel Effect |
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56 | (1) |
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Summary of
Chapters 2 and 3 |
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57 | (6) |
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59 | (1) |
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60 | (3) |
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Quantization of Energy in Simple Systems |
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63 | (26) |
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Bound States and Scattering States |
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63 | (3) |
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Stationary States of the Schrodinger Equation |
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64 | (1) |
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64 | (1) |
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65 | (1) |
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The One Dimensional Harmonic Oscillator |
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66 | (4) |
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Definition and Classical Motion |
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66 | (1) |
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The Quantum Harmonic Oscillator |
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67 | (2) |
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69 | (1) |
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70 | (5) |
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Relevance of Square Potentials |
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70 | (1) |
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Bound States in a One-Dimensional Square-Well Potential |
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71 | (2) |
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73 | (1) |
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Particle in a Three-Dimensional Box |
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74 | (1) |
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Periodic Boundary Conditions |
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75 | (3) |
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A One-Dimensional Example |
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75 | (2) |
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Extension to Three Dimensions |
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77 | (1) |
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Introduction of Phase Space |
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78 | (1) |
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The Double Well Problem and the Ammonia Molecule |
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78 | (6) |
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Model of the NH3 Molecule |
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79 | (1) |
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79 | (2) |
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81 | (1) |
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The Tunnel Effect and the Inversion Phenomenon |
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82 | (2) |
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Other Applications of the Double Well |
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84 | (5) |
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86 | (1) |
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87 | (2) |
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Principles of Quantum Mechanics |
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89 | (26) |
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90 | (2) |
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90 | (1) |
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Scalar Products and the Dirac Notations |
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90 | (1) |
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91 | (1) |
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92 | (1) |
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Operators in Hilbert Space |
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92 | (3) |
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Matrix Elements of an Operator |
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92 | (1) |
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Adjoint Operators and Hermitian Operators |
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93 | (1) |
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Eigenvectors and Eigenvalues |
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94 | (1) |
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Summary: Syntax Rules in Dirac's Formalism |
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95 | (1) |
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95 | (4) |
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95 | (1) |
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Projectors and Closure Relation |
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96 | (1) |
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The Spectral Decomposition of an Operator |
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96 | (1) |
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97 | (2) |
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Measurement of Physical Quantities |
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99 | (1) |
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Statement of the Principles of Quantum Mechanics |
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100 | (4) |
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Structure of Hilbert Space |
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104 | (3) |
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Tensor Products of Spaces |
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104 | (1) |
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The Appropriate Hilbert Space |
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105 | (1) |
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Properties of Tensor Products |
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105 | (1) |
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Operators in a Tensor Product Space |
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106 | (1) |
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106 | (1) |
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Reversible Evolution and the Measurement Process |
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107 | (8) |
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110 | (1) |
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111 | (4) |
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Two-State Systems, Principle of the Maser |
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115 | (20) |
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Two-Dimensional Hilbert Space |
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115 | (1) |
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A Familiar Example: the Polarization of Light |
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116 | (4) |
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Polarization States of a Photon |
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116 | (2) |
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Measurement of Photon Polarizations |
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118 | (1) |
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Successive Measurements and ``Quantum Logic'' |
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119 | (1) |
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The Model of the Ammonia Molecule |
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120 | (3) |
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Restriction to a Two-Dimensional Hilbert Space |
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120 | (1) |
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121 | (2) |
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123 | (1) |
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The Ammonia Molecule in an Electric Field |
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123 | (6) |
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The Coupling of NH3 to an Electric Field |
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124 | (1) |
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Energy Levels in a Fixed Electric Field |
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125 | (2) |
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Force Exerted on the Molecule by an Inhomogeneous Field |
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127 | (2) |
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Oscillating Fields and Stimulated Emission |
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129 | (2) |
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Principle and Applications of Masers |
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131 | (4) |
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131 | (1) |
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132 | (1) |
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132 | (1) |
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132 | (1) |
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133 | (2) |
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Commutation of Observables |
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135 | (22) |
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136 | (1) |
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137 | (1) |
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138 | (4) |
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Evolution of the Expectation Value of an Observable |
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138 | (1) |
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Particle in a Potential V(r) |
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139 | (1) |
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140 | (2) |
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142 | (6) |
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Existence of a Common Eigenbasis for Commuting Observables |
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142 | (1) |
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Complete Set of Commuting Observables (CSCO) |
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142 | (1) |
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Completely Prepared Quantum State |
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143 | (2) |
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Symmetries of the Hamiltonian and Search of Its Eigenstates |
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145 | (3) |
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Algebraic Solution of the Harmonic-Oscillator Problem |
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148 | (9) |
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148 | (1) |
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Annihilation and Creation Operators a and a† |
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148 | (1) |
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Eigenvalues of the Number Operator N |
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149 | (1) |
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150 | (1) |
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151 | (1) |
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152 | (5) |
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The Stern--Gerlach Experiment |
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157 | (20) |
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Principle of the Experiment |
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157 | (4) |
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157 | (2) |
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159 | (2) |
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The Quantum Description of the Problem |
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161 | (2) |
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The Observables μx and μy |
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163 | (2) |
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165 | (3) |
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Incompatibility of Measurements Along Different Axes |
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165 | (1) |
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Classical Versus Quantum Analysis |
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166 | (1) |
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Measurement Along an Arbitrary Axis |
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167 | (1) |
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Complete Description of the Atom |
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168 | (2) |
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168 | (1) |
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Representation of States and Observables |
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169 | (1) |
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Energy of the Atom in a Magnetic Field |
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170 | (1) |
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Evolution of the Atom in a Magnetic Field |
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170 | (5) |
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170 | (1) |
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Evolution in a Uniform Magnetic Field |
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171 | (2) |
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Explanation of the Stern--Gerlach Experiment |
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173 | (2) |
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175 | (2) |
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175 | (1) |
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176 | (1) |
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177 | (12) |
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177 | (6) |
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Definition of the Problem |
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177 | (1) |
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Power Expansion of Energies and Eigenstates |
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178 | (1) |
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First-Order Perturbation in the Nondegenerate Case |
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179 | (1) |
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First-Order Perturbation in the Degenerate Case |
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179 | (1) |
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First-Order Perturbation to the Eigenstates |
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180 | (1) |
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Second-Order Perturbation to the Energy Levels |
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181 | (1) |
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181 | (1) |
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Remarks on the Convergence of Perturbation Theory |
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182 | (1) |
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183 | (6) |
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183 | (1) |
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184 | (1) |
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Examples of Applications of the Variational Method |
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185 | (2) |
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187 | (2) |
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189 | (18) |
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Orbital Angular Momentum and the Commutation Relations |
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190 | (1) |
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Eigenvalues of Angular Momentum |
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190 | (6) |
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The Observables J2 and Jz and the Basis States |j, m> |
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191 | (1) |
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192 | (1) |
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Action of J± on the States |j, m> |
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192 | (1) |
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193 | (2) |
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195 | (1) |
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196 | (5) |
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The Quantum Numbers m and l are Integers |
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196 | (1) |
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197 | (1) |
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Eigenfunctions of L2 and Lz: the Spherical Harmonics |
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198 | (1) |
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Examples of Spherical Harmonics |
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199 | (1) |
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Example: Rotational Energy of a Diatomic Molecule |
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200 | (1) |
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Angular Momentum and Magnetic Moment |
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201 | (6) |
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Orbital Angular Momentum and Magnetic Moment |
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202 | (1) |
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Generalization to Other Angular Momenta |
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203 | (1) |
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What Should we Think about Half-Integer Values of j and m ? |
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204 | (1) |
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204 | (1) |
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205 | (2) |
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Initial Description of Atoms |
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207 | (24) |
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The Two-Body Problem; Relative Motion |
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208 | (2) |
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Motion in a Central Potential |
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210 | (5) |
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210 | (1) |
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Eigenfunctions Common to H, L2 and, Lz |
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211 | (4) |
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215 | (9) |
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Orders of Magnitude: Appropriate Units in Atomic Physics |
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215 | (1) |
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The Dimensionless Radial Equation |
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216 | (3) |
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219 | (1) |
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Stationary States of the Hydrogen Atom |
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220 | (1) |
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Dimensions and Orders of Magnitude |
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221 | (2) |
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Time Evolution of States of Low Energies |
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223 | (1) |
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224 | (1) |
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224 | (2) |
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226 | (5) |
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227 | (1) |
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228 | (3) |
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Spin 1/2 and Magnetic Resonance |
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231 | (18) |
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The Hilbert Space of Spin 1/2 |
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232 | (3) |
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233 | (1) |
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Representation in a Particular Basis |
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233 | (1) |
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234 | (1) |
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234 | (1) |
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Complete Description of a Spin-1/2 Particle |
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235 | (1) |
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235 | (1) |
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Representation of States and Observables |
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235 | (1) |
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236 | (2) |
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The Stern-Gerlach Experiment |
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236 | (1) |
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237 | (1) |
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Magnetic Moment of Elementary Particles |
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237 | (1) |
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Uncorrelated Space and Spin Variables |
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238 | (1) |
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239 | (10) |
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Larmor Precession in a Fixed Magnetic Field B0 |
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239 | (1) |
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Superposition of a Fixed Field and a Rotating Field |
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240 | (2) |
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242 | (2) |
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Applications of Magnetic Resonance |
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244 | (1) |
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Rotation of a Spin 1/2 Particle by 2π |
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245 | (1) |
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246 | (1) |
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247 | (2) |
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Addition of Angular Momenta, Fine and Hyperfine Structure of Atomic Spectra |
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249 | (24) |
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Addition of Angular Momenta |
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249 | (9) |
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The Total-Angular Momentum Operator |
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249 | (1) |
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Uncoupled and Coupled Bases |
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250 | (1) |
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A Simple Case: the Addition of Two Spins of 1/2 |
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251 | (3) |
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Addition of Two Arbitrary Angular Momenta |
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254 | (4) |
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One-Electron Atoms, Spectroscopic Notations |
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258 | (1) |
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Fine Structure of Monovalent Atoms |
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258 | (3) |
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Hyperfine Structure; the 21 cm Line of Hydrogen |
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261 | (12) |
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261 | (1) |
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262 | (1) |
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263 | (2) |
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The Effect of an External Magnetic Field |
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265 | (1) |
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The 21 cm Line in Astrophysics |
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265 | (3) |
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268 | (1) |
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268 | (5) |
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Entangled States, EPR Paradox and Bell's Inequality |
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273 | (20) |
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The EPR Paradox and Bell's Inequality |
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274 | (8) |
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``God Does not Play Dice'' |
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274 | (1) |
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275 | (3) |
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278 | (3) |
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281 | (1) |
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282 | (5) |
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The Communication Between Alice and Bob |
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282 | (3) |
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The Quantum Noncloning Theorem |
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285 | (1) |
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Present Experimental Setups |
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286 | (1) |
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287 | (6) |
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The Quantum Bits, or ``Q-Bits'' |
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287 | (1) |
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The Algorithm of Peter Shor |
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288 | (1) |
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Principle of a Quantum Computer |
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289 | (1) |
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290 | (1) |
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290 | (1) |
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291 | (2) |
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The Lagrangian and Hamiltonian Formalisms, Lorentz Force in Quantum Mechanics |
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293 | (16) |
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Lagrangian Formalism and the Least-Action Principle |
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294 | (3) |
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294 | (1) |
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295 | (2) |
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297 | (1) |
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Canonical Formalism of Hamilton |
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297 | (3) |
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297 | (1) |
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298 | (1) |
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299 | (1) |
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Analytical Mechanics and Quantum Mechanics |
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300 | (1) |
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Classical Charged Particles in an Electromagnetic Field |
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301 | (1) |
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Lorentz Force in Quantum Mechanics |
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302 | (7) |
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302 | (1) |
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303 | (1) |
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The Hydrogen Atom Without Spin in a Uniform Magnetic Field |
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304 | (1) |
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Spin-1/2 Particle in an Electromagnetic Field |
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305 | (1) |
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305 | (1) |
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305 | (4) |
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Identical Particles and the Pauli Principle |
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309 | (22) |
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Indistinguishability of Two Identical Particles |
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310 | (2) |
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Identical Particles in Classical Physics |
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310 | (1) |
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310 | (2) |
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Two-Particle Systems; the Exchange Operator |
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312 | (2) |
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The Hilbert Space for the Two Particle System |
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312 | (1) |
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The Exchange Operator Between Two Identical Particles |
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312 | (1) |
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313 | (1) |
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314 | (3) |
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The Case of Two Particles |
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314 | (1) |
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Independent Fermions and Exclusion Principle |
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315 | (1) |
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The Case of N Identical Particles |
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316 | (1) |
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317 | (1) |
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Physical Consequences of the Pauli Principle |
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317 | (14) |
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Exchange Force Between Two Fermions |
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318 | (1) |
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The Ground State of N Identical Independent Particles |
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318 | (2) |
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Behavior of Fermion and Boson Systems at Low Temperature |
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320 | (2) |
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Stimulated Emission and the Laser Effect |
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322 | (1) |
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Uncertainty Relations for a System of N Fermions |
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323 | (1) |
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Complex Atoms and Atomic Shells |
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324 | (2) |
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326 | (1) |
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327 | (4) |
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331 | (26) |
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Time-Dependent Perturbation Theory |
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332 | (4) |
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332 | (1) |
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332 | (1) |
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333 | (1) |
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First-Order Solution: the Born Approximation |
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334 | (1) |
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334 | (1) |
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Perturbative and Exact Solutions |
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335 | (1) |
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Interaction of an Atom with an Electromagnetic Wave |
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336 | (7) |
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The Electric-Dipole Approximation |
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336 | (1) |
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Justification of the Electric Dipole Interaction |
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337 | (1) |
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Absorptian of Energy by an Atom |
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338 | (1) |
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339 | (1) |
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339 | (2) |
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Control of Atomic Motion by Light |
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341 | (2) |
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343 | (7) |
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The Radioactivity of 57Fe |
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343 | (2) |
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345 | (1) |
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346 | (1) |
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347 | (3) |
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The Time-Energy Uncertainty Relation |
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350 | (7) |
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Isolated Systems and Intrinsic Interpretations |
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350 | (1) |
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Interpretation of Landau and Peierls |
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351 | (1) |
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The Einstein-Bohr Controversy |
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352 | (1) |
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353 | (1) |
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353 | (4) |
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357 | (24) |
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358 | (3) |
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Definition of Cross Section |
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358 | (1) |
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359 | (1) |
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360 | (1) |
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Quantum Calculation in the Born Approximation |
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361 | (6) |
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361 | (1) |
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362 | (1) |
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363 | (1) |
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Validity of the Born Approximation |
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364 | (1) |
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Example: the Yukawa Potential |
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365 | (1) |
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Range of a Potential in Quantum Mechanics |
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366 | (1) |
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Exploration of Composite Systems |
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367 | (5) |
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Scattering Off a Bound State and the Form Factor |
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367 | (1) |
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Scattering by a Charge Distribution |
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368 | (4) |
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General Scattering Theory |
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372 | (3) |
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372 | (1) |
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373 | (1) |
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The Integral Equation for Scattering |
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374 | (1) |
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375 | (6) |
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375 | (1) |
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Explicit Calculation of a Scattering Length |
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376 | (1) |
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The Case of Identical Particles |
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377 | (1) |
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378 | (1) |
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378 | (3) |
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Qualitative Physics on a Macroscopic Scale |
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381 | (16) |
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Confined Particles and Ground State Energy |
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382 | (4) |
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382 | (1) |
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383 | (1) |
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N-Fermion Systems and Complex Atoms |
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383 | (1) |
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Molecules, Liquids and Solids |
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384 | (1) |
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385 | (1) |
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Gravitational Versus Electrostatic Forces |
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386 | (6) |
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Screening of Electrostatic Interactions |
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386 | (1) |
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Additivity of Gravitational Interactions |
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387 | (1) |
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Ground State of a Gravity-Dominated Object |
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388 | (2) |
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Liquefaction of a Solid and the Height of Mountains |
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390 | (2) |
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White Dwarfs, Neutron Stars and the Gravitational Catastrophe |
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392 | (5) |
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White Dwarfs and the Chandrasekhar Mass |
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392 | (2) |
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394 | (2) |
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396 | (1) |
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Early History of Quantum Mechanics |
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397 | (10) |
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The Origin of Quantum Concepts |
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397 | (1) |
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397 | (1) |
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398 | (1) |
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398 | (2) |
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Empirical Regularities of Atomic Spectra |
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398 | (1) |
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399 | (1) |
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399 | (1) |
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400 | (1) |
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400 | (1) |
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401 | (2) |
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403 | (1) |
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The Mathematical Formalization |
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404 | (1) |
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Some Important Steps in More Recent Years |
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405 | (2) |
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406 | (1) |
| Appendix A Concepts of Probability Theory |
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407 | (10) |
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407 | (1) |
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2 Examples of Probability Laws |
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408 | (1) |
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408 | (1) |
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2.2 Continuous Probability Laws in One or Several Variables |
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408 | (1) |
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409 | (3) |
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409 | (1) |
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3.2 Conditional Probabilities |
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410 | (1) |
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3.3 Independent Random Variables |
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411 | (1) |
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3.4 Binomial Law and the Gaussian Approximation |
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411 | (1) |
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4 Moments of Probability Distributions |
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412 | (5) |
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4.1 Mean Value or Expectation Value |
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412 | (1) |
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4.2 Variance and Mean Square Deviation |
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412 | (1) |
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4.3 Bienayme--Tchebycheff Inequality |
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413 | (1) |
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4.4 Experimental Verification of a Probability Law |
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413 | (1) |
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414 | (3) |
| Appendix B. Dirac Distribution, Fourier Transformation |
|
417 | (12) |
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1 Dirac Distribution, or δ ``Function'' |
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417 | (3) |
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417 | (1) |
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1.2 Examples of Functions Which Tend to δ(x) |
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418 | (1) |
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419 | (1) |
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420 | (2) |
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420 | (1) |
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420 | (1) |
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2.3 Derivative of a Distribution |
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421 | (1) |
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422 | (1) |
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422 | (7) |
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422 | (1) |
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3.2 Fourier Transform of a Gaussian |
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423 | (1) |
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3.3 Inversion of the Fourier Transformation |
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423 | (1) |
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3.4 Parseval--Plancherel Theorem |
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424 | (1) |
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3.5 Fourier Transform of a Distribution |
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425 | (1) |
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426 | (1) |
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427 | (2) |
| Appendix C. Operators in Infinite-Dimensional Spaces |
|
429 | (6) |
|
1 Matrix Elements of an Operator |
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429 | (1) |
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430 | (5) |
| Appendix D. The Density Operator |
|
435 | (14) |
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436 | (3) |
|
1.1 A Mathematical Tool: the Trace of an Operator |
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|
436 | (1) |
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1.2 The Density Operator of Pure States |
|
|
437 | (1) |
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1.3 Alternative Formulation of Quantum Mechanics for Pure States |
|
|
438 | (1) |
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439 | (2) |
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2.1 A Particular Case: an Unpolarized Spin-1/2 System |
|
|
439 | (1) |
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2.2 The Density Operator for Statistical Mixtures |
|
|
440 | (1) |
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3 Examples of Density Operators |
|
|
441 | (3) |
|
3.1 The Micro-Canonical and Canonical Ensembles |
|
|
441 | (1) |
|
3.2 The Wigner Distribution of a Spinless Point Particle |
|
|
442 | (2) |
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|
|
444 | (5) |
|
4.1 Reduced Density Operator |
|
|
444 | (1) |
|
4.2 Evolution of a Reduced Density Operator |
|
|
444 | (1) |
|
4.3 Entanglement and Measurement |
|
|
445 | (1) |
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|
|
446 | (1) |
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|
|
446 | (3) |
| Solutions to the Exercises |
|
449 | (54) |
| Index |
|
503 | |
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