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| The Basic Approach | |
| Foundations | |
| The Premise | p. 2 |
| An absolute truth | |
| Difficult to believe | |
| Schroedinger's Equation | p. 3 |
| Packets | |
| The average position | |
| Matching velocities | |
| Operators | |
| Inventing the equation | |
| Light waves | p. 9 |
| The vector potential | |
| Maxwell's Equations | |
| New Meaning for Potentials | p. 10 |
| Aharanov and Bohm | |
| Measurement | p. 12 |
| Average values | |
| Consistent scenarios | |
| Eigenstates | p. 13 |
| Eigenvalues | |
| Normalization | |
| Energy levels | |
| Boundary conditions | p. 16 |
| Vanishing and periodic | |
| Sound Waves | p. 17 |
| Boundary conditions | |
| Modes | |
| Speed | |
| Simple Cases | |
| Free Electrons in One Dimension | p. 19 |
| Effect of boundary conditions | |
| [pi]-states in benzene | |
| Free Electron in Three Dimensions | p. 21 |
| Product wavefunctions | |
| The one-electron approximation | |
| Fermi surfaces | |
| Density of states | |
| Surface energies | |
| Quantum Slabs, Wires, and Dots | p. 24 |
| Giant Magnetoresistance | |
| Quantized conductance | |
| Circularly and Spherically-Symmetric Systems | p. 31 |
| Cylindrical and spherical systems | |
| Spherical harmonics | |
| Quantum wells | |
| Shallow wells | |
| The Harmonic Oscillator | p. 39 |
| Harmonic oscillator wavefunctions | |
| Ladder of energies | |
| Oscillators in three dimensions | |
| Hamiltonian Mechanics | |
| The Lagrangian | p. 45 |
| Lagrange's Equations | |
| Canonical momentum | |
| Hamilton's Equations | p. 46 |
| The equations | |
| Angular coordinates and angular momentum | |
| Restating the premise of quantum theory | |
| Including the Vector Potential | p. 48 |
| Fields from the vector potential | |
| Field energies | |
| Forces on charged particles | |
| The Schroedinger Equation with fields | |
| Electronic Structure | |
| Atoms | |
| The Hydrogen Atom | p. 53 |
| The ground state | |
| Excited states | |
| Many-Electron Atoms | p. 56 |
| The two-electron wavefunction | |
| Variational calculations | |
| The one-electron | |
| The Hartree and Hartree-Fock Approximations | |
| A table of atomic energy levels | |
| Pseudopotentials | p. 62 |
| The Periodic Table of the Elements | |
| Pseudowavefunctions | |
| Weak pseudopotentials | |
| Nuclear Structure | p. 65 |
| The liquid-drop model | |
| The shell model | |
| Structure of the nucleus | |
| Nuclear moments | |
| Beta and gamma rays | |
| Fission | |
| The Standard Model | |
| Molecules | |
| The Li[subscript 2] Molecule | p. 69 |
| LCAO or tight-binding states | |
| Bonding and antibonding states | |
| Dirac notation | |
| The Variational Method | p. 73 |
| Lowest-energy state | |
| Lagrange multipliers | |
| The variational equations | |
| Molecular Orbitals | p. 68 |
| Polar bonds | |
| Nonorthogonality and the overlap repulsion | |
| Perturbation Theory | p. 79 |
| First and second order | |
| Repulsion of levels | |
| N[subscript 2], CO, and CO[subscript 2] | p. 81 |
| Cohesion, [pi]-bonds | |
| Sp-hybrids and [sigma]-bonds | |
| Multicenter bonds | |
| Crystals | |
| The Linear Chain | p. 88 |
| S-bands | |
| The Brillouin Zone | |
| Benzene [pi]-bands | |
| The finite chain | |
| Free-Electron Bands and Tight-Binding Parameters | p. 92 |
| Matching the limits | |
| Universal coupling parameters | |
| P-state coupling | |
| Metallic, Ionic, and Covalent Solids | p. 98 |
| The Periodic Table and solids | |
| Metals and nonmetals | |
| Covalent semiconductors | |
| Ionic insulators | |
| D- and f-shell metals and compounds | |
| Time Dependence | |
| Transitions | |
| A Pair of Coupled States | p. 105 |
| The need for a continuum | |
| Fermi's Golden Rule | p. 106 |
| Derivation and interpretation | |
| Scattering in One and Three Dimensions | p. 109 |
| Scattering by impurities | |
| Tunneling | |
| Transmission in a 1-D Chain | p. 112 |
| Exact result | |
| Scattering and the high-transmission limit | |
| Tunneling and the low-transmission limit | |
| More General Barriers | p. 115 |
| Three dimensions | |
| Working through the barrier | |
| Free-electron formula | |
| Continuity equation and current operator | |
| General matching conditions | |
| Tunneling Systems | p. 120 |
| Tunneling as a quantum transition | |
| Metal-oxide-metal systems | |
| The scanning tunneling microscope | |
| Tunneling Resonance | p. 121 |
| Decay of states | |
| [alpha]-ray emission by nuclei | |
| Scattering resonances | |
| Resonant states and Coulomb blockades | |
| Transition Rates | |
| Second-Order Coupling | p. 125 |
| First-order states and second-order matrix elements | |
| Resonant tunneling | |
| Tunneling through impurity states | |
| Carrier Emission and Capture | p. 128 |
| Emission rate from the Golden Rule | |
| Capture from detailed balance | |
| Sequential tunneling compared with resonant tunneling | |
| Time-Dependent Perturbations | p. 128 |
| Fourier expansion of time dependence | |
| Energy loss and gain | |
| Optical Transitions | p. 130 |
| The interaction with light | |
| Selection rules | |
| Photon spin | |
| The ionization of an atom | |
| Beta-Ray Emission from Nuclei | p. 135 |
| The neutrino | |
| Fermi's theory | |
| Weak interactions | |
| Statistical Physics | |
| Statistical Mechanics | |
| Distribution Functions | p. 140 |
| Excitations of a harmonic oscillator | |
| Distribution of excitations and average excitation | |
| Phonon and Photon Statistics | p. 145 |
| Thermal distribution | |
| Lattice specific heat | |
| The Planck distribution | |
| Bosons | p. 147 |
| The chemical potential | |
| Bose-Einstein condensation | |
| Symmetry Under Interchange | p. 149 |
| Two-particle wavefunction | |
| Limitation on O[superscript 16 subscript 2] tumbling | |
| Ortho- and parahydrogen | |
| Fermions | p. 153 |
| Antisymmetry | |
| The Pauli Principle | |
| Fermi-Dirac distribution | |
| Classical limit | |
| Transport Theory | |
| Time-Dependent Distributions | p. 158 |
| Rate equations | |
| Detailed balance | |
| Steady state | |
| The Boltzmann Equation | p. 159 |
| Linearization | |
| Relaxation-time approximation | |
| Conductivity, etc. | p. 162 |
| Finding the distribution function | |
| Evaluating the current | |
| General transport properties | |
| Noise | |
| Classical Noise | p. 164 |
| Thermal or Johnson noise | |
| Fluctuations and dissipation | |
| Quantum Noise and van-der-Waals Interaction | p. 165 |
| Coupled dipole oscillators | |
| Correlated zero-point motion | |
| Many-body interaction | |
| Shot Noise | p. 167 |
| Shot noise in a classical gas | |
| Quantum suppression | |
| Enhancement | |
| Concentration | |
| Other Sources | p. 170 |
| Partition noise | |
| 1/f noise | |
| Electrons and Phonons | |
| Energy Bands | |
| The Empty-Core Pseudopotential | p. 174 |
| Form factors | |
| Structure factors | |
| A Band Calculation | p. 178 |
| Lattice wavenumbers | |
| Brillouin Zones | |
| Diagonalizing the Hamiltonian matrix | |
| Free-electron bands | |
| Diffraction | p. 184 |
| Finite pseudopotentials | |
| Fermi surfaces | |
| Scattering by Impurities | p. 185 |
| Total rates | |
| Momentum relaxation time | |
| Semiconductor Energy Bands | p. 186 |
| From pseudopotentials | |
| A tight-binding representation | |
| Electron Dynamics | |
| Dynamics of Packets | p. 189 |
| Hamilton's Equations | |
| Motion in a magnetic field | |
| Level crossing | |
| Effective Masses and Donor States | p. 192 |
| Effective-mass equations | |
| Anisotropic masses | |
| A hydrogenic donor state | |
| The Dynamics of Holes | p. 194 |
| Behavior as a positive-charge | |
| Positive-mass particle | |
| Binding electrons to form excitons | |
| Acceleration by fields and by elastic distortions | |
| Lattice Vibrations | |
| The Spectrum | p. 197 |
| One-dimensional chain | |
| Three-dimensional crystal | |
| The Classical-Vibration Hamiltonian | p. 201 |
| Normal coordinates | |
| Canonical momentum | |
| The Hamiltonian | |
| The Electron-Phonon Interaction | p. 203 |
| Structure factors | |
| Electron-phonon matrix elements | |
| Debye-Waller factor | |
| Quantum Optics | |
| Operators | |
| Annihilation and Creation Operators for Electrons | p. 207 |
| Many-particle states | |
| Commutation relations | |
| Operators for kinetic and potential energies | |
| Electron-electron interactions | |
| Stepping Operators | p. 212 |
| Guessing a form for the harmonic oscillator | |
| Commutation relations | |
| The number operator | |
| Normalization | |
| Excitation of the oscillator | |
| Angular Momentum | p. 216 |
| Raising and lowering operators | |
| Commutation relations | |
| Selection rules | |
| Phonons | |
| Annihilation and Creation Operators for Phonons | p. 220 |
| The Hamiltonian | |
| Commutation relations | |
| The electron-phonon interaction | |
| Phonon Emission and Absorption | p. 223 |
| Using the Golden Rule | |
| Eliminating operators | |
| Absorption | |
| Spontaneous emission | |
| Stimulated emission | |
| Polaron Self-Energy | p. 225 |
| Eliminating operators | |
| The polar coupling | |
| The polaron energy | |
| Electron-Electron and Nucleon-Nucleon Interactions | p. 228 |
| Interactions for superconductivity | |
| Semiconductors and exchange of virtual phonons | |
| Exchange of pions and the interaction between nucleons | |
| Photons | |
| Photons and the Electron-Photon Interaction | p. 232 |
| Normal coordinates | |
| Conjugate momentum | |
| The photon Hamiltonian | |
| Annihilation and creation operators | |
| Commutation relations | |
| Electron-photon interaction | |
| Excitation of Atoms | p. 235 |
| The matrix element | |
| Transition rates | |
| Equilibrium | |
| Saturating a transition | |
| The Three-Level Laser | p. 239 |
| Levels in helium | |
| Pumping | |
| Laser action | |
| Interband Transitions | p. 241 |
| Optical matrix elements | |
| Vertical transitions | |
| Light-emitting diodes | |
| Solid-state lasers | |
| Strain layers | |
| Coherent States | |
| Coherence in a Harmonic Oscillator | p. 247 |
| Mixed excitation levels | |
| Coherent phases | |
| A Driven Classical Oscillator | p. 249 |
| Polarizability | |
| Real and imaginary parts | |
| A Driven Quantum Oscillator | p. 251 |
| Dressed states | |
| Polarizability | |
| Energy loss | |
| Coherent Light | p. 254 |
| Coherence in a single mode | |
| Laser radiation | |
| Electromagnetically-Induced Transparency | p. 256 |
| The degenerate case | |
| Coupling and probe fields | |
| The nondegenerate case | |
| Dynamic states and the Rabi frequency | |
| Many-Body Effects | |
| Coulomb Effects | |
| Coulomb Shifts | p. 260 |
| Second ionization potentials | |
| Electron affinities | |
| Madelung contributions | |
| Band-gap enhancements | |
| Screening | p. 263 |
| Fermi-Thomas approximation | |
| The dielectric function | |
| Quantum screening | |
| Plasma oscillations | |
| Speed of sound in metals | |
| Cooperative Phenomena | |
| Localization and Symmetry Breaking | p. 270 |
| The Coulomb U and spin segregation | |
| Unrestricted Hartree-Fock | |
| First-order phase transitions | |
| The Hubbard Hamiltonian | p. 275 |
| The half-filled band | |
| Antiferromagnetic insulator | |
| Spin-density waves | |
| Second-order phase transitions | |
| Higher dimensions | |
| Special points | |
| Peierls Distortions | p. 281 |
| Pairing of atoms | |
| Charge-density wave | |
| Off-diagonal long-range order | |
| Superconductivity | p. 282 |
| Cooper pairs | |
| The BCS ground state | |
| Energy-gap parameter | |
| Persistent current | |
| Magnetism | |
| Free Electrons in a Magnetic Field | p. 287 |
| The Landau gauge | |
| Landau levels | |
| De Haas-van Alphen effect | |
| Quantum Hall Effect | |
| Magnetism of Atoms | p. 292 |
| The Hamiltonian | |
| Zeeman splitting | |
| The Bohr magneton and spin | |
| Spin resonance | |
| Nuclear Magnetic Resonance (NMR) | |
| Magnetic Susceptibility | p. 295 |
| Pauli paramagnetism of free electrons | |
| Comparison with the diamagnetic term | |
| Diamagnetism in atoms and molecules | |
| Molecular paramagnetism | |
| Ferromagnetism | p. 298 |
| Criterion for instability of a free-electron gas | |
| The Wigner crystal | |
| The atomic view of magnetic properties | |
| Spin-Orbit Coupling | p. 301 |
| The spin-orbit Hamiltonian | |
| Total angular momentum | |
| Fine structure for atoms | |
| Spin-split bands | |
| Anticrossings | |
| Shake-Off Excitations | |
| Adiabatic and Sudden Approximations | p. 306 |
| Time-dependent boundaries | |
| Transition probabilities | |
| A criterion for fast or slow | |
| Vibrational Excitations | p. 309 |
| A model system | |
| A criterion | |
| Transition and tunneling times | |
| The Franck-Condon Principle | |
| Polaron tunneling | |
| Phonon-assisted transitions | |
| The Mossbauer Effect | |
| Electronic and Auger processes | p. 315 |
| Beta-decay | |
| Donor states | |
| Atoms | |
| Shake-off in metals | |
| Inelastic Processes | p. 316 |
| Loss in an intermediate state | |
| Interference | |
| Random phases or collapse of wavefunctions | |
| Cloud-chamber tracks | |
| Qubits and quantum computing | |
| Quantum cryptography | |
| Epilogue | p. 322 |
| Exercises | p. 323 |
| References | p. 343 |
| Subject Index | p. 345 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9789810243753
ISBN-10: 9810243758
Published: 26th July 2000
Format: Hardcover
Language: English
Number of Pages: 370
Audience: College, Tertiary and University
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 22.86 x 15.24 x 2.24
Weight (kg): 0.67
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