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1 Twentieth-Century Quantum Mechanics |
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1 | (42) |
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1.1 Quantum Theory and Atomic Structure |
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1 | (15) |
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1.1.1 Wave Nature of Light |
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2 | (2) |
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1.1.2 Corpuscular Nature of Light |
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4 | (4) |
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1.1.3 Corpuscular Nature of the Electron |
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8 | (1) |
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1.1.4 Wave Nature of the Electron |
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9 | (2) |
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1.1.5 Early Models of Atomic Structure |
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11 | (5) |
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1.2 Probability and Statistical Mechanics |
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16 | (16) |
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1.2.1 Introduction to Probability |
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17 | (3) |
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1.2.2 Statistical Mechanics |
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20 | (3) |
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1.2.3 Combinatorial Analysis |
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23 | (4) |
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27 | (2) |
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1.2.5 Maxwell-Boltzmann Distribution |
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29 | (3) |
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1.3 The Birth of Quantum Mechanics |
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32 | (11) |
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36 | (7) |
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2 Mathematical Methods in Quantum Mechanics |
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43 | (42) |
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43 | (6) |
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2.2 Matrices in Quantum Mechanics |
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49 | (9) |
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2.3 Quantum Mechanics in Toy Hilbert Space |
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58 | (5) |
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2.4 The Hilbert Space of Real Wavefunctions |
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63 | (7) |
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70 | (5) |
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2.6 Complex Vector Spaces and Dirac Notation |
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75 | (4) |
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2.7 Coordinates and Momenta in Quantum Mechanics |
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79 | (4) |
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2.8 Heisenberg Uncertainty Principle |
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83 | (2) |
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3 The Schrodinger Equation |
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85 | (36) |
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85 | (3) |
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88 | (5) |
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3.3 The Harmonic Oscillator |
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93 | (3) |
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96 | (8) |
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96 | (2) |
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3.4.2 Angular Momentum Operators |
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98 | (1) |
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3.4.3 Eigenvalues and Eigenfunctions |
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99 | (3) |
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3.4.4 Matrix Representations |
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102 | (1) |
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102 | (1) |
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3.4.6 Abstract Theory of Angular Momentum |
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103 | (1) |
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104 | (7) |
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3.5.1 Spherical Polar Coordinates |
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105 | (1) |
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3.5.2 Solution of the Schrodinger Equation |
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106 | (3) |
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109 | (2) |
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3.6 Time Evolution and Collapse of the Wavefunction |
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111 | (6) |
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3.6.1 The Evolution Operator |
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111 | (2) |
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3.6.2 Schrodinger and Heisenberg Pictures |
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113 | (2) |
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3.6.3 Collapse of the Wavefunction |
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115 | (2) |
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3.7 Philosophical Issues in Quantum Mechanics |
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117 | (4) |
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4 New Adventures: Isotropic Vectors, Rotations, Spinors, and Groups |
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121 | (32) |
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4.1 In variance and the Objective World |
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121 | (5) |
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126 | (1) |
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4.3 The Stereographic Projection |
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127 | (10) |
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4.3.1 Spinors in Spherical Coordinates |
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136 | (1) |
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4.4 Lie Groups: SO(3) and Vector Rotation, SU(2) and Spinor Rotation |
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137 | (16) |
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5 Quantum Entanglement and Bell's Theorem |
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153 | (42) |
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5.1 Product States in Hilbert Space |
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153 | (7) |
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5.2 Bohm's Version of the Einstein--Podolsky--Rosen Experiment |
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160 | (4) |
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5.3 Hidden Variables and Bell's Inequality |
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164 | (5) |
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5.4 Generalized Bell's Inequality |
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169 | (4) |
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5.5 Maxwell's Equations, the Nature of Light, and All That |
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173 | (4) |
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5.6 Light Polarization and the Spin of the Photon |
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177 | (2) |
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5.7 The Hilbert Space of One Photon and Aspect's Experiment |
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179 | (5) |
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5.7.1 Photon Polarization |
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179 | (3) |
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5.7.2 Aspect's Experiment |
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182 | (2) |
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5.8 Measurement and Decoherence |
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184 | (11) |
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6 Digital and Quantum Computers |
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195 | (63) |
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195 | (1) |
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196 | (5) |
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198 | (3) |
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201 | (6) |
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201 | (4) |
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6.3.2 Binary Multiplication |
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205 | (2) |
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207 | (1) |
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207 | (9) |
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210 | (6) |
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216 | (2) |
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218 | (2) |
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6.7 Quantum Teleportation |
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220 | (2) |
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6.8 The Toffoli Logic Gate |
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222 | (2) |
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6.9 Quantum Fourier Transform |
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224 | (9) |
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230 | (3) |
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6.10 Some Results from Number Theory |
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233 | (21) |
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6.10.1 The Euclidean Algorithm |
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233 | (1) |
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234 | (1) |
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6.10.3 Modular Arithmetic |
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235 | (3) |
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6.10.4 Fermat's Little Theorem |
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238 | (2) |
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6.10.5 Chinese Remainder Theorem |
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240 | (2) |
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242 | (2) |
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6.10.7 Factorization of Large Numbers |
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244 | (4) |
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6.10.8 Quantum Order Finding |
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248 | (4) |
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6.10.9 Continued Fractions |
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252 | (1) |
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6.10.10 Prime Number Theorem |
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253 | (1) |
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6.11 Quantum Cryptography |
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254 | (4) |
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255 | (2) |
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257 | (1) |
Appendix |
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258 | (5) |
Bibliography |
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263 | (4) |
Index |
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267 | |