CONTENTS. vii. CHAPTER 2 Operators 15
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1 CHAPTER 1 Why Quantum Mechanics? Newtonian Mechanics and Classical Electromagnetism 1 (a) Newtonian Mechanics 1 (b) Electromagnetism Black Body Radiation The Heat Capacity of Solids and the Photoelectric Effect Photon Momentum and Compton Scattering Numerical Example Wave Aspects of Particles 8 Numerical Example 1.6 The Hydrogen Atom and the Bohr Model CHAPTER 2 Operators Mathematical Properties of Operators 15 (a) Definitions The Eigenfunctions and Eigenvalues of Operators Hermitian Operators Orthogonality of the Eigenfunctions of a Hermitian Operator Normalization of Eigenfunctions Completeness of Eigenfunctions Dirac Notation 20 Hermitian Adjoint Operators CHAPTER 3 The Basic Postulates of Quantum Mechanics The Basic Postulates of Quantum Mechanics The Average Value of an Observable 25 vii
2 3.3 The Form of Quantum Mechanical Operators 3.4 The Commutation Relation for the Momentum and Position Operators. Commuting Operators and Their Eigenfunctions 3.5 The Significance of 1f;(r) 3.6 The Eigenfunctions of the Energy Operators- The Schrõdinger Equation 3.7 The Uncertainty Principie 3.8 The Uncertainty Principie Applied to Electromagnetic Fields CHAPTER 4 One-Dimensional Energy Eigenvalue Infinite Potential Well 4.2 Finite Potential Well 4.3 Finite Potential Barrier 4.4 Physical Manifestation of Particle Tunneling: (a) a Decay of Nuclei (b) Tunneling in Solids CHAPTER 5 The Harmonic Oscillator Parity The Harmonic Oscillator 48 The Hermite Polynomials 50 The Harmonic Oscillator-Creation and Annihilation Operators The Annihilation and Creation Operators CHAPTER 6 The Quantum Mechanics of Angular Momentum The Angular Momentum Operators The Eigenfunctions and Eigenvalues of lz The Eigenfunctions and Eigenvalues of the Squared Magnitude of the Angular Momentum 62 The Normalization of Y,m( 8, </> ) 66 The Parity of Y,"( 8, </> ) viii
3 CHAPTER 7 Particles in Spherical Symmetric Potential Fields and the Hydrogen Atom A Particle in a Spherically Symmetric Potential Field The Hydrogenic Atom 72 The Eigenvalues 74 The Normalization Constant Nuclear Mass Correction of the Hydrogen Atom Problem 77 Recoil Energies and Doppler Shifts 80 Levei Degeneracy 81 Linear Combination of Eigenfunction Hybridized Wavefunctions and Molecular Bonding CHAPTER 8 Systems of Identical Particles 8.1 Systems of Two Electrons 8.2 The Helium Atom The First-Order Correction to Eo The Excited States CHAPTER 9 Matrix Formulation of Quantum Mechanics Some Basic Matrix Properties 95 The Unit Matrix 96 The Inverse Matrix 96 Hermitian Adjoint Matrices, Hermitian Matrices 96 Unitary Matrices Transformation of a Square Matrix Matrix Diagonalization Representations of Operators as Matrices 98 A Unitary Transformation Matrix Transformation of Operator Representations Deriving the Eigenfunctions and Eigenvalues of an Operator by the Matrix Method Matrix Elements of the Angular Momentum Operators Spin Angular Momentum Addition of Angular Momenta ix
4 CHAPTER 10 The Time-Dependent Schrodinger Equation 10.1 The Statistical Interpretation of I/;(r, t) 10.2 Expectation Values of Operators Ehrenfest's Theorem CHAPTER 11 Perturbation Theory lls 11.1 Time-Independent Perturbation Theory 115 First-Order Perturbation 116 Second-Order Perturbation Time-Dependent Perturbation Theory 118 Harmonic Perturbation 120 Step Function Perturbation 123 Limits of Validity of the Golden Rule The Density Matrix Formalism CHAPTER 12 The Interaction of Electromagnetic Radiation with Atomic Systems Some Basic Electromagnetic Background 127 The Energy of Electromagnetic Fields Quantization of Electromagnetic Modes 130 Electromagnetic Creation and Annihilation Operators 132 Traveling Wave Quantization Black-Body Radiation 133 Derivation of the Average Energy per Mode Induced Transitions in Collision Dominated Atomic Systems Spontaneous Transitions Quantum Mechanical Derivation of the Spontaneous Transition Rate A CHAPTER 13 Absorption and Dispersion of Radiation in Atomic Media The Time Evolution of a Collisionless Two-Level System Absorption and Amplification in Atomic Systems 152 X
5 13.3 Electric Polarization, Susceptibility, and the Dielectric Constant 154 The Significance of Xa( w) Density Matrix Derivation of the Atomic Susceptibility 158 The Significance of X'( w) CHAPTER 14 Laser Oscillation 14.1 Laser Oscillation The Fabry-Perot Laser The Laser Oscillation Frequencies The Ruby Laser Summary CHAPTER 15 Quantum Statistics The Three Types of Quantum Particles The Counting Algebra for Quantum Systems 179 (A) Identical but Distinguishable Particles 179 (B) Identical Indistinguishable Particles of Half-Odd Integral Spin-Fermions 180 (C) Identical, Indistinguishable Particles of Integral Spin-Bosons The Maxwell-Boltzmann, Fermi-Dirac, and Bose- Einstein Statistics 182 Case (A) Identical Distinguishable Particles 183 Case (B) Fermions 184 Case (C) Bosons Systems with More than One Constituent Evaluating the Parameter f3 in the Distribution Laws 186 Derivation of s, (15.38) CHAPTER 16 Some Specific Applications of the Statistical Distribution Laws The Maxwell-Boltzmann Distribution Fermi-Dirac Distribution The Bose-Einstein Distribution xi
6 CHAPTER 17 The Band Theory of Electrons in Crystals 17.1 The Kronig-Penney Model 17.2 The Multielectron Crystal 17.3 The Motion of Electrons in Crystals 17.4 The Control of Conductivity of Semiconductors by Impurities Current Flow in Semiconductors CHAPTER 18 The Interaction of Electrons and Nuclei with Magnetic Fields. Magnetic Resonance. The Maser 18.1 Orbital Magnetic Moments Numerical Example 18.2 Spin Angular Momentum 18.3 Nuclear Spins and Nuclear Magnetic Resonance 18.4 Hyperfine Interaction The H ydrogen Maser 18.5 Electron Paramagnetic Resonance CHAPTER 19 Charge Transport in Serniconductors Carriers in Intrinsic Semiconductors 237 Electron Density 238 The Density of Holes 239 Intrinsic Semiconductors The Ionization Energy of Impurity Atoms Carrier Concentration in Doped Semiconductors 246 "High" Temperature 247 "Low" Temperature Scattering of Electrons in Semiconductor Crystals Diffusion and Recombination 253 The Einstein Relation 254 Recombination of Electrons and Holes 256 The Carrier Transport Equation 257 Diffusion in a Semi-Infinite Slab xii
7 CHAPTER 20 Thep-n Semiconductor Junction. Thep-n-p Junction Transistor The Carrier and Potential Profiles in a p-n Junction 262 The Contact Potential cp The p-n Junction with an Applied Voltage 265 The Current Flow in p-n Junctions 267 Junction Fields and Capacitance The p-n-p Junction Transistor 271 The Transistor Currents CHAPTER 21 The Semiconductor Injection Laser Optical Absorption and Stimulated Emission in Semiconductors 280 Band-to-Band Transitions and Absorption in Semiconductors Bibliography 293 Index 295 xiii
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