| Introduction |
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1 | (1) |
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1 | (1) |
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Conventions Used in This Book |
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1 | (1) |
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2 | (1) |
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How This Book Is Organized |
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2 | (1) |
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Getting Started with Quantum Physics |
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2 | (1) |
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Round and Round with Angular Momentum and Spin |
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2 | (1) |
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Quantum Physics in Three Dimensions |
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2 | (1) |
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Acting on Impulse --- Impacts in Quantum Physics |
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3 | (1) |
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3 | (1) |
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3 | (1) |
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3 | (2) |
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Part I: Getting Started with Quantum Physics |
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5 | (90) |
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The Basics of Quantum Physics: Introducing State Vectors |
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7 | (30) |
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Describing the States of a System |
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7 | (5) |
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Becoming a Notation Meister with Bras and Kets |
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12 | (2) |
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Getting into the Big Leagues with Operators |
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14 | (4) |
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Introducing operators and getting into a healthy, orthonormal relationship |
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14 | (4) |
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Grasping Hermitian operators and adjoints |
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18 | (1) |
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Getting Physical Measurements with Expectation Values |
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18 | (3) |
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Commutators: Checking How Different Operators Really Are |
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21 | (2) |
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Simplifying Matters by Finding Eigenvectors and Eigenvalues |
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23 | (4) |
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Answers to Problems on State Vectors |
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27 | (10) |
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No Handcuffs Involved: Bound States in Energy Wells |
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37 | (32) |
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Starting with the Wave Function |
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37 | (3) |
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Determining Allowed Energy Levels |
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40 | (2) |
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Putting the Finishing Touches on the Wave Function by Normalizing It |
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42 | (2) |
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Translating to a Symmetric Square Well |
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44 | (1) |
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Banging into the Wall: Step Barriers When the Particle Has Plenty of Energy |
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45 | (3) |
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Hitting the Wall: Step Barriers When the Particle Has Doesn't Have Enough Energy |
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48 | (2) |
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Plowing through a Potential Barrier |
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50 | (4) |
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Answers to Problems on Bound States |
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54 | (15) |
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Over and Over with Harmonic Oscillators |
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69 | (26) |
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Total Energy: Getting On with a Hamiltonian |
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70 | (2) |
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Up and Down: Using Some Crafty Operators |
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72 | (2) |
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Finding the Energy after Using the Raising and Lowering Operators |
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74 | (2) |
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Using the Raising and Lowering Operators Directly on the Eigenvectors |
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76 | (1) |
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Finding the Harmonic Oscillator Ground State Wave Function |
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77 | (2) |
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Finding the Excited States' Wave Functions |
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79 | (3) |
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Looking at Harmonic Oscillators in Matrix Terms |
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82 | (3) |
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Answers to Problems on Harmonic Oscillators |
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85 | (10) |
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Part II: Round and Round with Angular Momentum and Spin |
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95 | (36) |
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Handling Angular Momentum in Quantum Physics |
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97 | (24) |
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Rotating Around: Getting All Angular |
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98 | (2) |
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Untangling Things with Commutators |
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100 | (2) |
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Nailing Down the Angular Momentum Eigenvectors |
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102 | (2) |
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Obtaining the Angular Momentum Eigenvalues |
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104 | (2) |
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Scoping Out the Raising and Lowering Operators' Eigenvalues |
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106 | (2) |
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Treating Angular Momentum with Matrices |
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108 | (4) |
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Answers to Problems on Angular Momentum |
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112 | (9) |
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Spin Makes the Particle Go Round |
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121 | (10) |
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Introducing Spin Eigenstates |
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121 | (3) |
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Saying Hello to the Spin Operators: Cousins of Angular Momentum |
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124 | (2) |
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Living in the Matrix: Working with Spin in Terms of Matrices |
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126 | (2) |
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Answers to Problems on Spin Momentum |
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128 | (3) |
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Part III: Quantum Physics in Three Dimensions |
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131 | (96) |
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Solving Problems in Three Dimensions: Cartesian Coordinates |
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133 | (28) |
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Taking the Schrodinger Equation to Three Dimensions |
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133 | (3) |
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Flying Free with Free Particles in 3-D |
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136 | (2) |
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Getting Physical by Creating Free Wave Packets |
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138 | (3) |
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Getting Stuck in a Box Well Potential |
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141 | (8) |
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Box potentials: Finding those energy levels |
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144 | (2) |
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Back to normal: Normalizing the wave function |
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146 | (3) |
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Getting in Harmony with 3-D Harmonic Oscillators |
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149 | (2) |
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Answers to Problems on 3-D Rectangular Coordinates |
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151 | (10) |
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Going Circular in Three Dimensions: Spherical Coordinates |
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161 | (22) |
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Taking It to Three Dimensions with Spherical Coordinates |
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162 | (5) |
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Dealing Freely with Free Particles in Spherical Coordinates |
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167 | (3) |
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Getting the Goods on Spherical Potential Wells |
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170 | (2) |
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Bouncing Around with Isotropic Harmonic Oscillators |
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172 | (3) |
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Answers to Problems on 3-D Spherical Coordinates |
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175 | (8) |
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Getting to Know Hydrogen Atoms |
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183 | (24) |
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Eyeing How the Schrodinger Equation Appears for Hydrogen |
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183 | (3) |
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Switching to Center-of-Mass Coordinates to Make the Hydrogen Atom Solvable |
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186 | (2) |
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Doing the Splits: Solving the Dual Schrodinger Equation |
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188 | (2) |
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Solving the Radial Schrodinger Equation for ψ(r) |
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190 | (5) |
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Juicing Up the Hydrogen Energy Levels |
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195 | (2) |
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Doubling Up on Energy Level Degeneracy |
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197 | (2) |
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Answers to Problems on Hydrogen Atoms |
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199 | (8) |
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Corralling Many Particles Together |
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207 | (20) |
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The 4-1-1 on Many-Particle Systems |
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207 | (2) |
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Zap! Working with Multiple-Electron Systems |
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209 | (2) |
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The Old Shell Game: Exchanging Particles |
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211 | (2) |
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Examining Symmetric and Antisymmetric Wave Functions |
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213 | (2) |
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Jumping into Systems of Many Distinguishable Particle |
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215 | (1) |
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Trapped in Square Wells: Many Distinguishable Particles |
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216 | (2) |
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Creating the Wave Functions of Symmetric and Antisymmetric Multi-Particle Systems |
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218 | (2) |
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Answers to Problems on Multiple-Particle Systems |
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220 | (7) |
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Part IV: Acting on Impulse --- Impacts in Quantum Physics |
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227 | (40) |
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Pushing with Perturbation Theory |
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229 | (16) |
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Examining Perturbation Theory with Energy Levels and Wave Functions |
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229 | (6) |
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Solving the perturbed Schrodinger equation for the first-order correction |
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231 | (2) |
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Solving the perturbed Schrodinger equation for the second-order correction |
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233 | (2) |
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Applying Perturbation Theory to the Real World |
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235 | (2) |
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Answers to Problems on Perturbation Theory |
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237 | (8) |
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One Hits the Other: Scattering Theory |
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245 | (22) |
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Cross Sections: Experimenting with Scattering |
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245 | (3) |
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A Frame of Mind: Going from the Lab Frame to the Center-of-Mass Frame |
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248 | (2) |
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Target Practice: Taking Cross Sections from the Lab Frame to the Center-of-Mass Frame |
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250 | (2) |
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Getting the Goods on Elastic Scattering |
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252 | (1) |
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The Born Approximation: Getting the Scattering Amplitude of Particles |
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253 | (3) |
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Putting the Born Approximation to the Test |
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256 | (2) |
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Answers to Problems on Scattering Theory |
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258 | (9) |
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267 | (16) |
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Ten Tips to Make Solving Quantum Physics Problems Easier |
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269 | (6) |
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Normalize Your Wave Functions |
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269 | (1) |
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269 | (1) |
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Meet the Boundary Conditions for Wave Functions |
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270 | (1) |
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Meet the Boundary Conditions for Energy Levels |
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270 | (1) |
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Use Lowering Operators to Find the Ground State |
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271 | (1) |
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Use Raising Operators to Find the Excited States |
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272 | (1) |
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273 | (1) |
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Decouple the Schrodinger Equation |
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274 | (1) |
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Use Two Schrodinger Equations for Hydrogen |
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274 | (1) |
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Take the Math One Step at a Time |
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274 | (1) |
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Ten Famous Solved Quantum Physics Problems |
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275 | (4) |
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275 | (1) |
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Enclosing Particles in a Box |
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275 | (1) |
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Grasping the Uncertainty Principle |
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276 | (1) |
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Eyeing the Dual Nature of Light and Matter |
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276 | (1) |
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Solving for Quantum Harmonic Oscillators |
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276 | (1) |
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Uncovering the Bohr Model of the Atom |
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276 | (1) |
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Tunneling in Quantum Physics |
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277 | (1) |
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Understanding Scattering Theory |
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277 | (1) |
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Deciphering the Photoelectric Effect |
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277 | (1) |
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Unraveling the Spin of Electrons |
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277 | (2) |
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Ten Ways to Avoid Common Errors When Solving Problems |
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279 | (4) |
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Translate between Kets and Wave Functions |
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279 | (1) |
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Take the Complex Conjugate of Operators |
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279 | (1) |
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Take the Complex Conjugate of Wave Functions |
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280 | (1) |
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Include the Minus Sign in the Schrodinger Equation |
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280 | (1) |
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Include sin θ in the Laplacian in Spherical Coordinates |
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280 | (1) |
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Remember that λ << 1 in Perturbation Hamiltonians |
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281 | (1) |
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Don't Double Up on Integrals |
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281 | (1) |
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Use a Minus Sign for Antisymmetric Wave Functions under Particle Exchange |
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281 | (1) |
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Remember What a Commutator Is |
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282 | (1) |
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Take the Expectation Value When You Want Physical Measurements |
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282 | (1) |
| Index |
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283 | |
Lisainfo e-raamatute kohta