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Readers' Orientation: Premise, and Design for the Study |
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1 | (12) |
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Philosophical Orientation |
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1 | (2) |
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3 | (3) |
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Physics Orientation: The Classical Bead on a Track |
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6 | (7) |
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The Quantum Bead on a Track: Its States and Representations |
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13 | (38) |
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What You Measure Is What You Know |
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13 | (1) |
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Degenerate and Nondegenerate Measurements |
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14 | (4) |
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An Event May Happen: There's an Amplitude for It |
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18 | (1) |
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The Pillar of Quantum Mechanics: Wave-Particle Duality |
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19 | (2) |
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The Pure Momentum State Wave Function |
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21 | (2) |
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Discrete and Continuous Spectra |
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23 | (8) |
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The Superposition of States |
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31 | (4) |
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A State Is a Point in Some Basis Space |
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35 | (16) |
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The Bead on a Track: Its Measurement Spectra Are Operator Eigenvalues |
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51 | (26) |
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Operators Operate on Kets |
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51 | (4) |
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Ket-Bra Sums Translate Operator Instructions |
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55 | (2) |
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Operators Have Eigenvalues |
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57 | (4) |
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Measurement Spaces Are Generated by Physical Operators |
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61 | (4) |
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To Solve the Problem, You May Choose Any Basis |
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65 | (3) |
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65 | (1) |
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66 | (1) |
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The Connection between Them |
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66 | (2) |
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A Degenerate Eigenvalue Is a State's Partial Label |
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68 | (9) |
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The Harmonic Oscillator: Bound Bead in a Symmetric Force Field |
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77 | (32) |
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The Hamiltonian with Hats Is the Energy Operator |
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77 | (1) |
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Cast the Problem into Position Space |
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78 | (6) |
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The Reflection Operator Reflects the Function |
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84 | (2) |
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In Position Space the Eigenvalue Problem Is a Boundary Value Problem |
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86 | (4) |
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The Problem May Be Cast into Momentum Space |
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90 | (1) |
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A Bracketed Operator Is a Matrix Element |
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91 | (1) |
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Hermitian Conjugation Is a Matrix Element Rule |
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92 | (2) |
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The Commutator Is an Operator |
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94 | (2) |
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The Lowering Operator Annihilates One Unit of Energy |
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96 | (13) |
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The Bead in a Spherical Shell: Two Dimensions with Angular Momentum |
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109 | (38) |
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109 | (5) |
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Vector Operator: One with Operator Components |
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114 | (5) |
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Compatible Operators Always Commute |
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119 | (5) |
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What Produces Angular Momentum Is the Angular Momentum Operator |
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124 | (3) |
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Angular Momentum: Its Operators and Eigenvalues |
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127 | (5) |
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Raising and Lowering Operator Instructions |
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132 | (1) |
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Orbital Angular Momentum States Have a Position-Space Representation |
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133 | (5) |
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Raising and Lowering Operators Generate the Spherical Harmonics |
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138 | (9) |
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Spin, Matrices, and the Structure of Quantum Mechanics |
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147 | (30) |
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Magnetic Moment Signals Angular Momentum |
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147 | (3) |
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Because Angular Momentum Is Quantized, Magnetic Moments Have Discrete Spectra |
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150 | (2) |
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The Electron Spin Quantum Number Is 1/2 |
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152 | (1) |
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The Spin Operator Is the Half-Unit Angular Momentum Operator |
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153 | (4) |
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The Transformation Matrix: Amplitudes for All Possible Experimental Results |
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157 | (3) |
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Matrices Solve the Eigenvalue Problem in Finite Basis Spaces |
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160 | (2) |
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The Ket-Bra Sum Is Matrix Multiplication |
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162 | (4) |
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Diagonalizing a Matrix Is a Mechanical Procedure |
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166 | (5) |
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For Physical States the Transformation Matrix Is Unitary |
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171 | (6) |
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177 | (36) |
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Particle Energy Expresses Wave Frequency |
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179 | (2) |
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The Time Evolution Operator: Energy Eigenstates Are Its Home Space |
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181 | (1) |
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A Neutron in a Magnetic Field: Its State Evolves in Time |
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182 | (4) |
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The Schroedinger Equation: Differential Evolution in Time |
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186 | (3) |
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The Classical Limit of Quantum Mechanics: What Happens on the Average |
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189 | (1) |
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Invariants Commute with the Hamiltonian |
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190 | (3) |
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Angular Momentum Vector Operators Rotate as Their Vector Counterparts Do |
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193 | (6) |
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Two Systems Interact: They Exchange Energy |
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199 | (3) |
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The Exponential of an Operator-Sum: Time Manufactures Order |
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202 | (3) |
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Fermi's Golden Rule Is the Transition Probability per Unit Time |
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205 | (8) |
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The Simplest Atom: Two Particles Bound Together |
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213 | (36) |
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A Central Field Potential May Bind Two Particles |
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214 | (1) |
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Decoupling the Hamiltonian Replaces Old Particles By New Ones |
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215 | (4) |
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The Particle-through-a-Box Has Periodic Boundary Conditions |
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219 | (5) |
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Energy-Compatible Operators Label the Eigenstates |
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224 | (2) |
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The Electrostatic Central Field Governs Hydrogen |
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226 | (4) |
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The Grand Result Is a 6-D State |
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230 | (2) |
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A State Is Defined by Its Labels |
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232 | (2) |
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A Product Wave Function Signifies Discernible Particles |
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234 | (1) |
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There Exist Conditional States |
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235 | (2) |
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Measurement Creates Reality |
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237 | (12) |
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Indistinguishable Particles: Identical Bosons, and Identical Fermions |
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249 | (36) |
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Exchangeable Is Indistinguishable |
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250 | (1) |
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An Operator Effects Exchange |
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251 | (4) |
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The Eigenvalues of Exchange: Bosons and Fermions |
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255 | (6) |
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There Are No Spinless Fermions |
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261 | (2) |
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From Two Spins, a Net Spin |
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263 | (2) |
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The Ideal Gas: Noninteracting Particles |
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265 | (6) |
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An Indistinguishable Particle Gas: Think in Distribution Space |
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271 | (3) |
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The Slater Determinant Constructs Fermi States |
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274 | (1) |
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Never Two Indistinguishable Fermions in the Same Single-Particle State |
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274 | (11) |
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Stationary-State Perturbation Theory |
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285 | (18) |
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The Answer Comes from Nearly-the-Answer |
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285 | (2) |
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First-Order Nondegenerate Result: The New Operator Between Old States |
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287 | (1) |
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A Null Result in First Order: Sum over Intermediate States |
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288 | (1) |
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Degenerate States, First Order: Set the Determinate to Zero |
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289 | (5) |
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Derivation of the Perturbation Theory Results |
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294 | (9) |
| Epilogue So What? |
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303 | (8) |
| Index |
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311 | |
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