Preface to the Second Edition | p. xi |
The Dawn of the Quantum Theory | p. 1 |
Blackbody Radiation | p. 2 |
Planck's Quantum Hypothesis | p. 4 |
The Photoelectric Effect | p. 8 |
Vibrations of Atoms in Crystals | p. 11 |
The Hydrogen Atomic Spectrum | p. 12 |
The Rydberg Formula | p. 15 |
Angular Momentum | p. 16 |
Quantized Angular Momentum | p. 18 |
Reduced Mass | p. 22 |
De Broglie Waves | p. 26 |
The Relation between de Broglie Waves and Quantized Angular Momentum | p. 28 |
De Broglie Waves Observed | p. 29 |
Two-Slit Experiments | p. 30 |
The Heisenberg Uncertainty Principle | p. 34 |
Problems | p. 36 |
References | p. 44 |
Complex Numbers | p. 45 |
Problems | p. 49 |
The Classical Wave Equation | p. 53 |
The One-Dimensional Classical Wave Equation | p. 54 |
Separation of Variables | p. 54 |
Oscillatory Solutions to Differential Equations | p. 58 |
Superposition of Normal Modes | p. 61 |
A Vibrating Membrane | p. 64 |
Interference of Waves | p. 68 |
Problems | p. 72 |
References | p. 84 |
Probability and Statistics | p. 85 |
Problems | p. 93 |
The Schrodinger Equation and a Particle in a Box | p. 97 |
The Schrodinger Equation | p. 97 |
Linear Operators in Quantum Mechanics | p. 99 |
Eigenvalue Problems In Quantum Mechanics | p. 101 |
Wave Functions and Their Probabilistic Interpretation | p. 103 |
Quantized Energies | p. 105 |
Normalized Wave Functions | p. 107 |
Average Quantities in Quantum Mechanics | p. 110 |
The Uncertainty Principle and Operators | p. 112 |
Particle in a Three-Dimensional Box | p. 114 |
Problems | p. 120 |
References | p. 128 |
Vectors | p. 129 |
Problems | p. 139 |
The Postulates and General Principles of Quantum Mechanics | p. 143 |
State Functions | p. 143 |
Quantum-Mechanical Operators and Classical Variables | p. 147 |
Observable Quantities and Eigenvalues | p. 149 |
Commutators and the Uncertainty Principle | p. 153 |
Hermitian Operators | p. 156 |
Hermitian Operators and Orthogonality | p. 160 |
Commuting Operators and Mutual Eigenfunctions | p. 164 |
Probabilty of a Measurement and Fourier Coefficients | p. 165 |
The Time-Dependent Schrodinger Equation | p. 170 |
Quantum Mechanics and the Two-Slit Experiment | p. 175 |
Problems | p. 179 |
References | p. 196 |
Series and Limits | p. 197 |
Problems | p. 202 |
The Harmonic Oscillator and Vibrational Spectroscopy | p. 207 |
Classical Harmonic Oscillator | p. 207 |
Conservation of Energy of a Classical Harmonic Oscillator | p. 210 |
Harmonic-Oscillator Model of a Diatomic Molecule | p. 213 |
The Harmonic-Oscillator Approximation | p. 215 |
The Energy Levels of a Quantum-Mechanical Harmonic Oscillator | p. 218 |
Infrared Spectra of Diatomic Molecules | p. 219 |
Overtones in Vibrational Spectra | p. 222 |
Harmonic-Oscillator Wave Functions | p. 225 |
Parity of Hermite Polynomials | p. 228 |
Relations Among Hermite Polynomials | p. 230 |
Normal Coordinates | p. 233 |
Harmonic-Oscillator Selection Rule | p. 237 |
Operator Method Solution to the Schrodinger Equation for a Harmonic Oscillator | p. 239 |
Problems | p. 243 |
References | p. 254 |
Spherical Coordinates | p. 255 |
Problems | p. 263 |
The Rigid Rotator and Rotational Spectroscopy | p. 267 |
The Energy Levels of a Rigid Rotator | p. 267 |
The Rigid Rotator Model of a Diatomic Molecule | p. 272 |
Rotation-Vibrational Spectra | p. 275 |
Rotation-Vibration Interaction | p. 278 |
A Nonrigid Rotator | p. 281 |
Spherical Harmonics | p. 282 |
Rigid-Rotator Selection Rule | p. 288 |
Angular Momentum and Measurements | p. 290 |
Determination of the Eigenvalues of L[superscript 2] and L[subscript z] by Operator Methods | p. 296 |
Problems | p. 300 |
References | p. 308 |
Determinants | p. 309 |
Problems | p. 317 |
The Hydrogen Atom | p. 321 |
The Schrodinger Equation for a Hydrogen Atom | p. 321 |
s Orbitals | p. 327 |
p Orbitals | p. 334 |
The Zeeman Effect | p. 339 |
Electron Spin | p. 344 |
Spin-Orbit Interaction | p. 349 |
Hydrogen Atomic Term Symbols | p. 353 |
The Zeeman Effect Revisited | p. 357 |
The Schrodinger Equation for a Helium Atom | p. 359 |
Problems | p. 360 |
References | p. 366 |
Matrices | p. 367 |
Problems | p. 376 |
Approximation Methods | p. 381 |
The Variational Method | p. 381 |
Trial Functions That Depend Linearly on Variational Parameters | p. 387 |
Trial Functions That Depend Nonlinearly on Variational Parameters | p. 395 |
Introduction to Perturbation Theory | p. 396 |
First-Order Pertubation Theory | p. 399 |
Selection Rules and Time-Dependent Perturbation Theory | p. 404 |
Problems | p. 410 |
References | p. 426 |
Matrix Eigenvalue Problems | p. 427 |
Problems | p. 432 |
Many-Electron Atoms | p. 435 |
Atomic Units | p. 435 |
Classic Calculations on a Helium Atom | p. 439 |
Hartree-Fock Equations for a Helium Atom | p. 444 |
Antisymmetry of Electronic Wave Functions | p. 447 |
Slater Determinants | p. 450 |
The Hartree-Fock-Roothaan Method | p. 453 |
Hartree-Fock-Roothaan Results for Atoms | p. 458 |
Correlation Energy | p. 463 |
Atomic Term Symbols | p. 466 |
Addition of Angular Momenta | p. 470 |
Hund's Rules | p. 474 |
Atomic Term Symbols and Atomic Spectra | p. 475 |
Russell-Saunders Coupling | p. 479 |
An SCF Calculation of a Helium Atom | p. 482 |
Problems | p. 489 |
References | p. 497 |
The Chemical Bond: One- and Two-Electron Molecules | p. 499 |
The Born-Oppenheimer Approximation | p. 500 |
The Hydrogen Molecular Ion, [Characters not reproducible] | p. 501 |
Molecular Orbitals Constructed from a Linear Combination of Atomic Orbitals | p. 506 |
Bonding and Antibonding Orbitals | p. 513 |
Molecular Orbital Theory and the Virial Theorem | p. 515 |
Polarization Terms in Basis Sets | p. 521 |
The Schrodinger Equation for H[subscript 2] | p. 523 |
Molecular Orbital Theory Results for H[subscript 2] | p. 526 |
Configuration Interaction | p. 531 |
An SCF Calculation on H[subscript 2] | p. 537 |
Molecular Orbital Theory of H[subscript 2] | p. 543 |
Problems | p. 547 |
References | p. 557 |
Qualitative Theory of Chemical Bonding | p. 559 |
Molecular Orbitals | p. 560 |
Molecular Electron Configurations | p. 564 |
Molecular Orbital Theory and Heteronuclear Diatomic Molcules | p. 570 |
Molecular Term Symbols | p. 573 |
Molecular Term Symbols and Symmetry Properties | p. 577 |
The [pi]-Electron Approximation | p. 581 |
Huckel Molecular Orbital Theory and Bond Orders | p. 588 |
Huckel Molecular Orbital Theory in Matrix Notation | p. 595 |
Problems | p. 597 |
References | p. 605 |
The Hartree-Fock-Roothaan Method | p. 607 |
The Hartree-Fock-Roothaan Equations | p. 608 |
Minimal Gaussian Basis Sets | p. 614 |
Extended Gaussian Basis Sets | p. 621 |
Basis Sets with Orbital Polarization Terms | p. 626 |
Using Gaussian 03 and WebMO | p. 631 |
Hartree-Fock-Roothaan Results | p. 636 |
Post-Hartree-Fock Methods | p. 643 |
Problems | p. 653 |
References | p. 660 |
References for Post-Hartree-Fock Methods | p. 660 |
Answers to the Numerical Problems | p. 663 |
Index | p. 683 |
Illustration Credits | p. 690 |
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