Google full text of our books:

# Quantum Mechanics in a NutshellGerald D. Mahan

 TABLE OF CONTENTS:Preface xiChapter 1: Introduction 11.1 Introduction 11.2 Schrödinger's Equation 21.3 Eigenfunctions 41.4 Measurement 81.5 Representations 81.5.1 Schrödinger Representation 91.5.2 Heisenberg Representation 101.6 Noncommuting Operators 11Chapter 2: One Dimension 142.1 Square Well 142.2 Linear Potentials 262.3 Harmonic Oscillator 292.4 Raising and Lowering Operators 342.5 Exponential Potential 392.5.1 Bound State 402.5.2 Continuum State 422.6 Delta-Function Potential 452.7 Number of Solutions 482.8 Normalization 492.8.1 Bound States 492.8.2 Box Normalization 502.8.3 Delta-Function Normalization 512.8.4 The Limit of Infinite Volume 542.9 Wave Packets 56Chapter 3: Approximate Methods 623.1 WKBJ 623.2 Bound States by WKBJ 683.2.1 Harmonic Oscillator 713.2.2 Morse Potential 713.2.3 Symmetric Ramp 733.2.4 Discontinuous Potentials 743.3 Electron Tunneling 763.4 Variational Theory 773.4.1 Half-Space Potential 803.4.2 Harmonic Oscillator in One Dimension 82Chapter 4: Spin and Angular Momentum 874.1 Operators, Eigenvalues, and Eigenfunctions 874.1.1 Commutation Relations 884.1.2 Raising and Lowering Operators 894.1.3 Eigenfunctions and Eigenvalues 904.2 Representations 954.3 Rigid Rotations 1004.4 The Addition of Angular Momentum 102Chapter 5: Two and Three Dimensions 1085.1 Plane Waves in Three Dimensions 1085.2 Plane Waves in Two Dimensions 1125.3 Central Potentials 1145.3.1 Central Potentials in 3D 1145.3.2 Central Potential in 2D 1185.4 Coulomb Potentials 1195.4.1 Bound States 1195.4.2 Confluent Hypergeometric Functions 1215.4.3 Hydrogen Eigenfunctions 1215.4.4 Continuum States 1255.5 WKBJ 1265.5.1 Three Dimensions 1265.5.2 3D Hydrogen Atom 1275.5.3 Two Dimensions 1285.6 Hydrogen-like Atoms 1305.6.1 Quantum Defect 1315.6.2 WKBJ Derivation 1325.6.3 Expectation Values 1345.7 Variational Theory 1345.7.1 Hydrogen Atom: n 1 1355.7.2 Hydrogen Atom: l 1 1365.7.3 Helium Atom 1375.8 Free Particles in a Magnetic Field 1435.8.1 Gauges 1435.8.2 Eigenfunctions and Eigenvalues 1445.8.3 Density of States 1465.8.4 Quantum Hall Effect 1475.8.5 Flux Quantization 150Chapter 6: Matrix Methods and Perturbation Theory 1576.1 H and H0 1576.2 Matrix Methods 1586.2.1 2 x 2 1606.2.2 Coupled Spins 1606.2.3 Tight-Binding Model 1636.3 The Stark Effect 1666.4 Perturbation Theory 1706.4.1 General Formulas 1706.4.2 Harmonic Oscillator in Electric Field 1746.4.3 Continuum States 1766.4.4 Green's Function 1806.5 The Polarizability 1816.5.1 Quantum Definition 1826.5.2 Polarizability of Hydrogen 1836.6 Van der Waals Potential 1886.7 Spin-Orbit Interaction 1946.7.1 Spin-Orbit in Atoms 1956.7.2 Alkali Valence Electron in Electric Field 1996.8 Bound Particles in Magnetic Fields 2026.8.1 Magnetic Susceptibility 2046.8.2 Alkali Atom in Magnetic Field 2056.8.3 Zeeman Effect 2076.8.4 Paschen-Back Effect 209Chapter 7: Time-Dependent Perturbations 2137.1 Time-Dependent Hamiltonians 2137.2 Sudden Approximation 2157.2.1 Shake-up and Shake-off 2167.2.2 Spin Precession 2187.3 Adiabatic Approximation 2207.4 Transition Rates: The Golden Rule 2227.5 Atomic Excitation by a Charged Particle 2267.6 Born Approximation to Scattering 2317.6.1 Cross Section 2327.6.2 Rutherford Scattering 2357.6.3 Electron Scattering from Hydrogen 2367.7 Particle Decay 237Chapter 8: Electromagnetic Radiation 2448.1 Quantization of the Field 2458.1.1 Gauges 2468.1.2 Lagrangian 2508.1.3 Hamiltonian 2538.1.4 Casimir Force 2568.2 Optical Absorption by a Gas 2588.2.1 Entangled Photons 2688.3 Oscillator Strength 2698.4 Polarizability 2738.5 Rayleigh and Raman Scattering 2788.6 Compton Scattering 283Chapter 9: Many-Particle Systems 2889.1 Introduction 2889.2 Fermions and Bosons 2899.2.1 Two Identical Particles 2909.3 Exchange Energy 2919.3.1 Two-Electron Systems 2919.3.2 Parahelium and Orthohelium 2939.3.3 Hund's Rules 2939.4 Many-Electron Systems 2959.4.1 Evaluating Determinants 2959.4.2 Ground-State Energy 2979.4.3 Hartree-Fock Equations 2999.4.4 Free Electrons 3019.4.5 Pair Distribution Function 3039.4.6 Correlation Energy 3049.4.7 Thomas-Fermi Theory 3049.4.8 Density Functional Theory 3079.5 Second Quantization 3099.5.1 Bosons 3099.5.2 Fermions 3129.6 Bose-Einstein Condensation 3139.6.1 Noninteracting Particles 3139.6.2 Off-Diagonal Long-Range Order 314Chapter 10: Scattering Theory 32010.1 Elastic Scattering 32010.1.1 Partial Wave Analysis 32310.1.2 Scattering in Two Dimensions 32610.1.3 Hard-Sphere Scattering 32810.1.4 Ramsauer-Townsend Effect 33010.1.5 Born Approximation 33210.2 Scattering of Identical Particles 33310.2.1 Two Free Particles 33310.2.2 Electron Scattering from Hydrogen 33510.3 T-Matrices 33710.4 Distorted Wave Scattering 34010.5 Scattering from Many Particles 34310.5.1 Bragg Scattering 34310.5.2 Scattering by Fluids 34410.5.3 Strong Scattering 34610.6 Wave Packets 34710.6.1 Three Dimensions 34710.6.2 Scattering by Wave Packets 348Chapter 11: Relativistic Quantum Mechanics 35211.1 Four-Vectors 35211.2 Klein-Gordon Equation 35411.2.1 Derivation 35411.2.2 Free Particle 35411.2.3 Currents and Densities 35511.2.4 Step Potential 35611.2.5 Nonrelativistic Limit 35611.2.6 П-Mesonic Atoms 35711.3 Dirac Equation 36011.3.1 Derivation 36111.3.2 Current and Charge Density 36411.3.3 Gamma-Matrices 36411.3.4 Free-Particle Solutions 36611.3.5 Spin-Projection Operators 36911.3.6 Scattering of Dirac Particles 37111.4 Antiparticles and Negative Energy States 37411.5 Spin Averages 37711.6 Nonrelativistic Limit 37911.6.1 First Approximation 37911.6.2 Second Approximation 38011.6.3 Relativistic Corrections for Hydrogenic States 38211.7 Relativistic Interactions 38411.7.1 Photon Green's Function 38411.7.2 Electron Green's Function 38711.7.3 Boson Exchange 38711.8 Scattering of Electron and Muon 388Index 397Return to Book DescriptionFile created: 4/21/2017 Questions and comments to: webmaster@press.princeton.eduPrinceton University Press