Preface |
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Chapter 1 Visualization of Wave Functions |
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1 | (14) |
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1 | (1) |
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1.2 Visualization of Complex Numbers |
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2 | (7) |
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1.3 Visualization of Complex-Valued Functions |
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9 | (4) |
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1.4 Special Topic: Wave Functions with an Inner Structure |
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13 | (2) |
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Chapter 2 Fourier Analysis |
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15 | (34) |
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2.1 Fourier Series of Complex-Valued Functions |
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16 | (5) |
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2.2 The Hilbert Space of Square-Integrable Functions |
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21 | (4) |
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2.3 The Fourier Transformation |
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25 | (3) |
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2.4 Basic Properties of the Fourier Transform |
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28 | (1) |
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29 | (5) |
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2.6 Further Results About the Fourier Transformation |
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34 | (4) |
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38 | (3) |
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41 | (4) |
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2.9 Special Topic: Dirac Delta Distribution |
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45 | (4) |
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49 | (34) |
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3.1 The Free Schrodinger Equation |
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50 | (5) |
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55 | (4) |
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3.3 The Free Time Evolution |
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59 | (4) |
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3.4 The Physical Meaning of a Wave Function |
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63 | (7) |
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70 | (2) |
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3.6 Special Topic: Asymptotic Time Evolution |
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72 | (3) |
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3.7 Schrodinger Cat States |
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75 | (5) |
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3.8 Special Topic: Energy Representation |
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80 | (3) |
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Chapter 4 States and Observables |
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83 | (24) |
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4.1 The Hilbert Space of Wave Functions |
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84 | (2) |
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4.2 Observables and Linear Operators |
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86 | (3) |
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4.3 Expectation Value of an Observable |
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89 | (2) |
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91 | (2) |
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4.5 The Commutator of x and p |
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93 | (1) |
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4.6 Electromagnetic Fields |
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94 | (3) |
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97 | (3) |
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100 | (4) |
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4.9 Transition Probability |
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104 | (3) |
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Chapter 5 Boundary Conditions |
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107 | (28) |
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108 | (2) |
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5.2 Other Boundary Conditions |
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110 | (1) |
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111 | (3) |
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5.4 Eigenvalues and Eigenfunctions |
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114 | (5) |
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5.5 Special Topic: Unit Function in a Dirichlet Box |
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119 | (5) |
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124 | (1) |
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5.7 The Double Slit Experiment |
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125 | (5) |
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5.8 Special Topic: Analysis of the Double Slit Experiment |
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130 | (5) |
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Chapter 6 Linear Operators in Hilbert Spaces |
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135 | (22) |
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6.1 Hamiltonian and Time Evolution |
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135 | (3) |
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138 | (1) |
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6.3 Unitary Time Evolution and Unitary Groups |
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139 | (2) |
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141 | (2) |
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143 | (1) |
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6.6 Self-Adjointness and Stone's Theorem |
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144 | (3) |
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147 | (2) |
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149 | (2) |
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6.9 Canonical Commutation Relations |
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151 | (1) |
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6.10 Commutator and Uncertainty Relation |
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152 | (1) |
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6.11 Symmetries and Conservation Laws |
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153 | (4) |
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Chapter 7 Harmonic Oscillator |
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157 | (34) |
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7.1 Basic Definitions and Properties |
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158 | (5) |
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7.2 Eigenfunction Expansion |
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163 | (4) |
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7.3 Solution of the Initial-Value Problem |
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167 | (4) |
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7.4 Time Evolution of Observables |
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171 | (4) |
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7.5 Motion of Gaussian Wave Packets |
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175 | (2) |
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7.6 Harmonic Oscillator in Two and More Dimensions |
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177 | (2) |
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7.7 Theory of the Harmonic Oscillator |
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179 | (5) |
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7.8 Special Topic: More About Coherent States |
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184 | (3) |
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7.9 Special Topic: Mehler Kernel |
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187 | (4) |
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Chapter 8 Special Systems |
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191 | (36) |
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8.1 The Free Fall in a Constant Force Field |
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192 | (4) |
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8.2 Free Fall with Elastic Reflection at the Ground |
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196 | (4) |
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8.3 Magnetic Fields in Two Dimensions |
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200 | (2) |
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8.4 Constant Magnetic Field |
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202 | (3) |
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8.5 Energy Spectrum in a Constant Magnetic Field |
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205 | (2) |
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8.6 Translational Symmetry in a Magnetic Field |
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207 | (6) |
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8.7 Time Evolution in a Constant Magnetic Field |
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213 | (5) |
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8.8 Systems with Rotational Symmetry in Two Dimensions |
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218 | (4) |
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8.9 Spherical Harmonic Oscillator |
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222 | (2) |
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8.10 Angular Momentum Eigenstates in a Magnetic Field |
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224 | (3) |
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Chapter 9 One-Dimensional Scattering Theory |
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227 | (30) |
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227 | (4) |
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9.2 Example: Potential Step |
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231 | (3) |
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9.3 Wave Packets and Eigenfunction Expansion |
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234 | (2) |
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9.4 Potential Step: Asymptotic Momentum Distribution |
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236 | (3) |
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239 | (2) |
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241 | (5) |
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246 | (2) |
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9.8 Example: Potential Well |
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248 | (3) |
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251 | (6) |
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Appendix A Numerical Solution in One Dimension |
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257 | (6) |
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263 | (12) |
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263 | (1) |
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264 | (1) |
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265 | (1) |
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266 | (2) |
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268 | (2) |
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270 | (2) |
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272 | (3) |
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Appendix C Other Books on Quantum Mechanics |
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275 | (4) |
Index |
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279 | |