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Preface | p. xiii |
Author | p. xvii |
Quantum Principles | |
Perspective and Principles | p. 3 |
Prelude to Quantum Mechanics | p. 3 |
Stern-Gerlach Experiment | p. 7 |
Idealized Stern-Gerlach Results | p. 12 |
Classical Model Attempts | p. 15 |
Wave Functions for Two Physical-Outcome Case | p. 21 |
Process Diagrams, Operators, and Completeness | p. 25 |
Further Properties of Operators | p. 28 |
Operator Reformulation | p. 37 |
Operator Rotation | p. 39 |
Bra-Ket Notation/Basis States | p. 46 |
Transition Amplitudes | p. 47 |
Three-Magnet Setup Example-Coherence | p. 50 |
Hermitian Conjugation | p. 53 |
Unitary Operators | p. 56 |
A Very Special Operator | p. 57 |
Matrix Representations | p. 58 |
Matrix Wave Function Recovery | p. 62 |
Expectation Values | p. 64 |
Wrap Up | p. 65 |
Problems | p. 66 |
Particle Motion in One Dimension | p. 77 |
Photoelectric Effect | p. 77 |
Compton Effect | p. 79 |
Uncertainty Relation for Photons | p. 83 |
Stability of Ground States | p. 85 |
Bohr Model | p. 86 |
Fourier Transform and Uncertainty Relations | p. 88 |
Schrödinger Equation | p. 90 |
Schrödinger Equation Example | p. 94 |
Dirac Delta Functions | p. 97 |
Wave Functions and Probability | p. 99 |
Probability Current | p. 102 |
Time Separable Solutions | p. 103 |
Completeness for Particle States | p. 104 |
Particle Operator Properties | p. 107 |
Operator Rules | p. 110 |
Time Evolution and Expectation Values | p. 112 |
Wrap-Up of Chapter 2 | p. 114 |
Problems | p. 115 |
Some One-Dimensional Solutions to the Schrödinger Equation | p. 121 |
Introduction | p. 121 |
The Infinite Square Well: Differential Solution | p. 123 |
The Infinite Square Well: Operator Solution | p. 129 |
The Finite Potential Barrier Step Potential | p. 134 |
The Harmonic Oscillator | p. 140 |
The Attractive Kronig-Penny Model | p. 149 |
Bound State and Scattering Solutions | p. 155 |
Problems | p. 156 |
Hilbert Space and Unitary Transformations | p. 161 |
Introduction and Notation | p. 161 |
Inner and Outer Operator Products | p. 163 |
Operator-Matrix Relationship | p. 165 |
Hermitian Operators and Eigenkets | p. 166 |
Gram-Schmidt Orthogonalization Process | p. 168 |
Compatible Operators | p. 170 |
Uncertainty Relations and Incompatible Operators | p. 172 |
Simultaneously Measureable Operators | p. 175 |
Unitary Transformations and Change of Basis | p. 176 |
Coordinate Displacements and Unitary Transformations | p. 180 |
Schrödinger and Heisenburg Pictures of Time Evolution | p. 181 |
Free Gaussian Wave Packet in the Heisenberg Picture | p. 184 |
Potentials and the Ehrenfest Theorem | p. 185 |
Problems | p. 186 |
Three Static Approximation Methods | p. 191 |
Introduction | p. 191 |
Time-Independent Perturbation Theory | p. 192 |
Examples of Time-Independent Perturbation Theory | p. 195 |
Aspects of Degenerate Perturbation Theory | p. 198 |
WKB Semiclassical Approximation | p. 198 |
Use of the WKB Approximation in Barrier Penetration | p. 202 |
Use of the WKB Approximation in Bound States | p. 204 |
Variational Methods | p. 207 |
Problems | p. 212 |
Generalization to Three Dimensions | p. 217 |
Cartesian Basis States and Wave Functions in Three Dimensions | p. 217 |
Position/Momentum Eigenket Generation | p. 219 |
Example: Three-Dimensional Infinite Square Well | p. 222 |
Spherical Basis States | p. 224 |
Orbital Angular Momentum Operator | p. 225 |
Effect of Angular Momentum on Basis States | p. 226 |
Energy Eigenvalue Equation and Angular Momentum | p. 230 |
Complete Set of Observables for the Radial Schrödinger Equation | p. 232 |
Specification of Angular Momentum Eigenstates | p. 234 |
Angular Momentum Eigenvectors and Spherical Harmonics | p. 240 |
Completeness and Other Properties of Spherical Harmonics | p. 245 |
Radial Eigenfunctions | p. 248 |
Problems | p. 248 |
Quantum Particles | |
The Three-Dimensional Radial Equation | p. 255 |
Recap of the Situation | p. 255 |
The Free Particle | p. 257 |
The Infinite Spherical Well Potential | p. 264 |
The "Deuteron" | p. 267 |
The Coulomb Potential: Initial Considerations | p. 280 |
The Coulomb Potential: 2-D Harmonic Oscillator Comparison | p. 283 |
The Confined Coulombic Model | p. 299 |
Problems | p. 307 |
Addition of Angular Momenta | p. 317 |
General Angular-Momentum Eigenstate Properties | p. 317 |
Combining Angular Momenta for Two Systems | p. 319 |
Explicit Example of Adding Two Spin 1/2 Systems | p. 324 |
Explicit Example of Adding Orbital Angular Momentum and Spin 1/2 | p. 326 |
Hydrogen Atom and the Choice of Basis States | p. 331 |
Hydrogen Atom and Perturbative Energy Shifts | p. 334 |
Problems | p. 338 |
Spin and Statistics | p. 343 |
The Connection between Spin and Statistics | p. 343 |
Building Wave Functions with Identical Particles | p. 344 |
Particle Occupation Basis | p. 347 |
More on Fermi-Dirac Statistics | p. 352 |
Interaction Operator and Feynman Diagrams | p. 354 |
Implications of Detailed Balance | p. 357 |
Cubical Enclosures and Particle States | p. 362 |
Maxwell-Boltzman Statistics | p. 364 |
Bose-Einstein Statistics | p. 366 |
Fermi-Dirac Statistics | p. 370 |
The Hartree-Fock Equations | p. 375 |
Problems | p. 379 |
Quantum Particle Scattering | p. 387 |
Introduction | p. 387 |
The One-Dimensional Integral Schrödinger Equation | p. 388 |
Reflection and Transmission Amplitudes | p. 392 |
One-Dimensional Delta-Function Scattering | p. 393 |
Step-Function Potential Scattering | p. 396 |
The Born Series | p. 402 |
The Three-Dimensional Integral Schrödinger Equation | p. 404 |
The Helmholtz Equation and Plane Waves | p. 407 |
Cross Sections and the Scattering Amplitude | p. 411 |
Scattering Phase Shifts | p. 412 |
Finite-Range Potential Scattering | p. 416 |
The Three-Dimensional Born Series | p. 421 |
Identical Particle Scattering | p. 426 |
Proton-Proton Scattering | p. 430 |
Problems | p. 434 |
Connecting to the Standard Model | p. 443 |
Discrete Symmetries | p. 443 |
Parity | p. 444 |
Time Reversal | p. 448 |
Charge Conjugation | p. 453 |
Particle Primer | p. 454 |
Particle Interactions | p. 460 |
Quantum Electrodynamics | p. 461 |
Quantum Chromodynamics | p. 463 |
Weak Interactions | p. 468 |
Supersymmetry | p. 472 |
Superstrings | p. 474 |
Postlude | p. 477 |
Helpful Books on Particle and String Physics | p. 477 |
Problems | p. 478 |
Notation Comments and Comparisons | p. 485 |
Lattice Models | p. 487 |
2-D Harmonic Oscillator Wave Function Normalization | p. 493 |
Allowed Standard Model Interactions | p. 495 |
The Ising Model and More | p. 497 |
Weak Flavor Mixing | p. 509 |
Index | p. 523 |
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