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**Note:** Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.

{chapter}{1}The Origins of Quantum Mechanics, 1 {1.1}Introduction, 1 {1.2}Blackbody Radiation, 2 The Problem with Blackbody Radiation, 2 {1.3}The Nature of Light, 10 The Photoelectric Effect, 10 The Compton Effect, 13 Is it a Particle or a Wave?, 15 {1.4}The Wave Nature of Matter, 16 {1.5}The Bohr Atom, 17 {1.6}Where do we Stand?, 20 {chapter}{2}Math Interlude A: Complex Numbers and Linear Operators, 23 {2.1}Complex Numbers, 23 {2.2}Operators, 30 Definition of an Operator, 30 Eigenfunctions and Eigenvalues, 31 {chapter}{3}The Schr\"odinger Equation, 35 {3.1}Derivation of the Schr\"odinger Equation, 35 {3.2}The Meaning of the Wave Function, 44 {3.3}The Time-Independent Schr\"odinger Equation, 51 {Derivation of the Time-Independent Schr\"odinger Equation, 51 {Qualitative Solutions and the Origin of Quantization, 53 {chapter}{4}One-dimensional Time-independent Schr\"odinger Equation, 63 {4.1}Unbound States: Scattering and Tunneling, 63 Scattering From Step-Function Potentials, 68 Step-function Potential With $E > V_0$, 69 Step-function Potential With $E<V_0$, 74 Tunneling, 76 {4.2}Bound Systems, 79 The Infinite Square Well, 80 The Harmonic Oscillator Potential, 83 {chapter}{5}Math Interlude B: Linear Algebra, 95 {5.1}Properties of Linear Operators, 95 {5.2}Vector Spaces, 100 Inner Products, 101 Adjoint and Hermitian Operators, 105 Basis Sets, 107 {chapter}{6}The Three-dimensional Time-independent Schr\"odinger Equation, 113 {6.1}Solution in Rectangular Coordinates, 114 {6.2}Angular Momentum, 117 {6.3}The Schr\"odinger Equation in Spherical Coordinates, 125 {6.4}The Hydrogen Atom, 133 {chapter}{7}Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function, 145 {7.1}The Matrix Formulation of Linear Operators, 145 {7.2}Dirac Notation, 151 {7.3}The Dirac Delta Function, 153 {chapter}{8}Spin Angular Momentum, 159 {8.1}Spin Operators, 159 {8.2}Evidence for Spin, 160 {8.3}Adding Angular Momentum, 164 {8.4}The Matrix Representation of Spin, 166 {8.5}The Stern--Gerlach Experiment, 173 {8.6}Spin Precession, 176 {8.7}Spin Systems with Two Particles, 180 Noninteracting Spins, 180 Interacting Spins, 183 {8.8}Measurement Theory, 186 Hidden Variables, 188 The Many Worlds Interpretation of Quantum Mechanics, 189 {chapter}{9}Time-Independent Perturbation Theory, 195 {9.1}Derivation of Time-Independent Perturbation Theory, 195 {9.2}Perturbations to the Atomic Energy Levels, 204 Fine Structure, 205 The Lamb Shift, 212 {9.3}The Atom in External Electric or Magnetic Fields, 214 The Atom in an Electric Field: The Stark Effect, 214 The Atom in a Magnetic Field: The Zeeman Effect, 216 {chapter}{10}The Variational Principle, 225 {10.1}Variational Principle: Theory, 225 {10.2}Variational Principle: Application to the Helium Atom, 230 {chapter}{11}Time-dependent Perturbation Theory, 237 {11.1}Derivation of Time-dependent Perturbation Theory, 237 {11.2}Application: Selection Rules for Electromagnetic Radiation, 247 {chapter}{12}Scattering Theory, 257 {12.1}Definition of the Cross Section, 257 {12.2}The Born Approximation, 262 {12.3}Partial Waves, 271 {chapter}{13}The Multiparticle Schr\"odinger Equation, 281 {13.1}Wave Function for Identical Particles, 281 {13.2}Multielectron Atoms, 293 {chapter}{14}Some Modern Applications of Quantum Mechanics, 303 {14.1}Magnetic Resonance Imaging, 303 {14.2}Quantum Computing, 308 {chapter}{15}What Comes Next? Relativistic Quantum Mechanics, 313 {15.1}The Klein--Gordon Equation, 313 Derivation of the Klein--Gordon Equation, 313 Probability Densities and Currents, 314 {15.2}The Dirac Equation, 317

Library of Congress Subject Headings for this publication:

Quantum theory -- Textbooks.