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Preface | |

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Stern-Gerlach Experiments | |

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The Original Stern-Gerlach Experiment | |

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Four Experiments | |

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The Quantum State Vector | |

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Analysis of Experiment 3 | |

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Experiment 5 | |

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Summary | |

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Rotation of Basis States and Matrix Mechanics | |

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The Beginnings of Matrix Mechanics | |

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Rotation Operators | |

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The Identity and Projection Operators | |

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Matrix Representations of Operators | |

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Changing Representations | |

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Expectation Values | |

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Photon Polarization and the Spin of the Photon | |

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Summary | |

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Angular Momentum | |

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Rotations Do Not Commute and Neither Do the Generators | |

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Commuting Operators | |

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The Eigenvalues and Eigenstates of Angular Momentum | |

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The Matrix Elements of the Raising and Lowering Operators | |

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Uncertainty Relations and Angular Momentum | |

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The Spin-1/2 Eigenvalue Problem | |

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A Stern-Gerlach Experiment with Spin-1 Particles | |

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Summary | |

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Time Evolution | |

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The Hamiltonian and the Schrodinger Equation | |

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Time Dependence of Expectation Values | |

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Precession of a Spin-1/2 Particle in a Magnetic Field | |

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Magnetic Resonance | |

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The Ammonia Molecule and the Ammonia Maser | |

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The Energy-Time Uncertainty Relation | |

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Summary | |

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A System of Two Spin-1/2 Particles | |

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The Basis States for a System of Two Spin-1/2 Particles | |

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The Hyperfine Splitting of the Ground State of Hydrogen | |

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The Addition of Angular Momenta for Two Spin-1/2 Particles | |

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The Einstein-Podolsky-Rosen Paradox | |

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A Nonquantum Model and the Bell Inequalities | |

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Summary | |

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Wave Mechanics in One Dimension | |

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Position Eigenstates and the Wave Function | |

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The Translation Operator | |

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The Generator of Translations | |

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The Momentum Operator in the Position Basis | |

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Momentum Space | |

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A Gaussian Wave Packet | |

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The Heisenberg Uncertainty Principle | |

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General Properties of Solutions to the Schrodinger Equation in Position Space | |

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The Particle in a Box | |

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Scattering in One Dimension | |

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Summary | |

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The One-Dimensional Harmonic Oscillator | |

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The Importance of the Harmonic Oscillator | |

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Operator Methods | |

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An Example: Torsional Oscillations of the Ethylene Molecule | |

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Matrix Elements of the Raising and Lowering Operators | |

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Position-Space Wave Functions | |

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The Zero-Point Energy | |

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The Classical Limit | |

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Time Dependence | |

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Solving the Schrodinger Equation in Position Space | |

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Inversion Symmetry and the Parity Operator | |

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Summary | |

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Path Integrals | |

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The Multislit, Multiscreen Experiment | |

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The Transition Amplitude | |

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Evaluating the Transition Amplitude for Short Time Intervals | |

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The Path Integral | |

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Evaluation of the Path Integral for a Free Particle | |

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Why Some Particles Follow the Path of Least Action | |

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Quantum Interference Due to Gravity | |

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Summary | |

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Translational and Rotational Symmetry in the Two-Body Problem | |

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The Elements of Wave Mechanics in Three Dimensions | |

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Translational Invariance and Conservation of Linear Momentum | |

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Relative and Center-of-Mass Coordinates | |

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Estimating Ground-State Energies Using the Uncertainty Principle | |

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Rotational Invariance and Conservation of Angular Momentum | |

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A Complete Set of Commuting Observables | |

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Vibrations and Rotations of a Diatomic Molecule | |

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Position-Space Representations of L in Spherical Coordinates | |

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Orbital Angular Momentum Eigenfunctions | |

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Summary | |

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Bound States of Central Potentials | |

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The Behavior of the Radial Wave Function Near the Origin | |

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The Coulomb Potential and the Hydrogen Atom | |

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The Finite Spherical Well and the Deuteron | |

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The Infinite Spherical Well | |

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The Three-Dimensional Isotropic Harmonic Oscillator | |

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Conclusion | |

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Time-Independent Perturbations | |

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Nondegenerate Perturbation Theory | |

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An Example Involving the One-Dimensional Harmonic Oscillator | |

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Degenerate Perturbation Theory | |

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The Stark Effect in Hydrogen | |

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The Ammonia Molecule in an External Electric Field Revisited | |

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Relativistic Perturbations to the Hydrogen Atom | |

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The Energy Levels of Hydrogen, Including Fine Structure, the Lamb Shift, and Hyperfine Splitting | |

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The Zeeman Effect in Hydrogen | |

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Summary | |

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Identical Particles | |

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Indistinguishable Particles in Quantum Mechanics | |

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The Helium Atom | |

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Multielectron Atoms and the Periodic Table | |

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Covalent Bonding | |

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Conclusion | |

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Scattering | |

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The Asymptotic Wave Function and the Differential Cross Section | |

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The Born Approximation | |

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An Example of the Born Approximation: The Yukawa Potential | |

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The Partial Wave Expansion | |

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Examples of Phase-Shift Analysis | |

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Summary | |

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Photons and Atoms | |

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The Aharonov-Bohm Effect | |

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The Hamiltonian for the Electromagnetic Field | |

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Quantizing the Radiation Field | |

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The Properties of Photons | |

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The Hamiltonian of the Atom and the Electromagnetic Field | |

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Time-Dependent Perturbation Theory | |

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Fermi's Golden Rule | |

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Spontaneous Emission | |

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Higher-Order Processes and Feynman Diagrams | |

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Appendixes | |

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Electromagnetic Units | |

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The Addition of Angular Momenta | |

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Dirac Delta Functions | |

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Gaussian Integrals | |

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The Lagrangian for a Charge q in a Magnetic Field | |

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Values of Physical Constants | |

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Answers to Selected Problems | |

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Index | |