About the Authors |
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vii | |
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xiii | |
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xv | |
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xvii | |
Preface |
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xxv | |
Acknowledgments |
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xxvii | |
Introduction |
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xxix | |
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1 Introduction to Superposition Principle Waves |
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1 | (10) |
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1 | (10) |
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2 The Wave Function, Expectations Values, and Uncertainty |
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11 | (26) |
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2.1 The Foundations of Quantum Mechanics |
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11 | (14) |
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2.2 The Postulates of Quantum Mechanics |
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25 | (6) |
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2.3 Uncertainty and Expectation Values |
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31 | (1) |
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2.4 Compatibility Condition Between Observable |
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32 | (1) |
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2.5 Relation of Indeterminacy |
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33 | (1) |
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34 | (3) |
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3 The Schrodinger Equation |
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37 | (18) |
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37 | (1) |
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3.2 Symmetry Transformations |
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37 | (2) |
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3.3 Equation of Motion of a Free Particle |
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39 | (1) |
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3.4 Temporal Evolution Pictures |
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39 | (6) |
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3.5 Solutions of the Schrodinger Equation |
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45 | (10) |
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55 | (8) |
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55 | (1) |
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55 | (8) |
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63 | (12) |
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63 | (1) |
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5.2 The Quantum Measurement |
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64 | (11) |
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6 Path Integral Formulation of Quantum Mechanics |
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75 | (18) |
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6.1 Calculating the Transition Amplitude |
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77 | (2) |
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6.2 Interpretation of the Classical Limit |
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79 | (4) |
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6.3 Functional Integrals and Properties |
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83 | (10) |
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7 Supersymmetry in Quantum Mechanics |
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93 | (20) |
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7.1 Construction of the Supersymmetric Partners |
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96 | (3) |
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7.2 Algebra of a Supersymmetric System |
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99 | (4) |
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7.3 Violation of the Supersymmetry |
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103 | (6) |
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7.4 Successive Factoring of a Hamiltonian |
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109 | (4) |
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8 Quantum Persistent Currents |
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113 | (50) |
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113 | (3) |
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8.2 Persistent Charge Currents |
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116 | (3) |
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8.3 Persistent Spin Currents |
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119 | (3) |
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8.4 Equilibrium Currents in a Mesoscopic Ring Coupled to a Reservoir |
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122 | (1) |
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8.5 The Decoupled SO Active Ring |
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122 | (2) |
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8.6 Decoherence with Spin Orbit Coupling |
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124 | (6) |
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8.7 Persistent Charge Currents |
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130 | (6) |
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8.8 Persistent Spin Currents |
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136 | (3) |
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8.9 Equilibrium Currents in a Mesoscopic Graphene Ring |
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139 | (4) |
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8.10 Ring Hamiltonian and Boundary Conditions |
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143 | (3) |
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8.11 Closing the Wave Function on a Graphene Ring |
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146 | (2) |
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148 | (5) |
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8.13 Charge Persistent Currents |
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153 | (6) |
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8.14 Equilibrium Spin Currents |
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159 | (2) |
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8.15 Velocity Operators for Graphene |
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161 | (2) |
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9 Cryptography and Quantum Mechanics |
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163 | (30) |
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9.1 Classical Cryptography |
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163 | (5) |
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168 | (2) |
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9.3 Heisenberg Uncertainty Principle |
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170 | (2) |
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172 | (7) |
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179 | (14) |
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10 Non-Equilibrium Quantum Mechanics |
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193 | (18) |
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10.1 Systems in Equilibrium |
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193 | (7) |
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10.2 Systems Out of Equilibrium |
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200 | (11) |
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11 Introductory Spintronics |
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211 | (26) |
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211 | (4) |
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11.2 Effects Associated to Spintronics |
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215 | (1) |
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11.3 Giant Magnetic Resistance |
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216 | (4) |
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220 | (1) |
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11.5 Magnetic Tunnel Junction |
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221 | (2) |
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11.6 Julliere Model for TMR |
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223 | (2) |
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11.7 Spin Torque Momentum |
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225 | (4) |
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11.8 Semiconductor Spintronics |
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229 | (8) |
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237 | (14) |
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12.1 Structure of Quantum Dots |
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238 | (13) |
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251 | (18) |
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13.1 Spin 1/2 Hilbert Space |
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252 | (2) |
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13.2 Complete Description of a 1/2 Spin Particle |
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254 | (2) |
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13.3 Magnetic Spin Moment |
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256 | (2) |
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13.4 Spatial and Spin Uncorrected Variables |
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258 | (1) |
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13.5 The Magnetic Resonance |
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258 | (11) |
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14 Introductory Theory of Scattering |
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269 | (16) |
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14.1 Amplitude of Scattering ·(k, θ φ) |
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270 | (6) |
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276 | (3) |
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14.3 The Scattering Operator, the S Matrix |
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279 | (2) |
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14.4 Partial Waves Theory for Central Potentials |
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281 | (4) |
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15 Introduction to Quantum Hall Effect |
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285 | (28) |
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15.1 Classical Hall Effect |
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285 | (7) |
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15.2 Two-Dimensional Electronic Systems |
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292 | (12) |
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15.3 The Quantum Hall Effect---Integer Quantum Hall Effect |
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304 | (9) |
Bibliography |
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313 | (8) |
Index |
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321 | |