CHAPTER 1 Historical Review 1 Blackbody Radiation and Planck’s Formula 1 The Photoelectric Effect 6 The Bohr Theory of the Atom 7 de Broglie’s Hypothesis 10 Quiz 11
CHAPTER 2 Basic Developments 13 The Schrödinger Equation 13 Solving the Schrödinger Equation 18 The Probability Interpretation and Normalization 24 Expansion of the Wavefunction and Finding Coefficients 35 The Phase of a Wavefunction 44 Operators in Quantum Mechanics 46 Momentum and the Uncertainty Principle 54 The Conservation of Probability 59 Quiz 63
CHAPTER 3 The Time Independent Schrödinger Equation 65 The Free Particle 66 Bound States and 1-D Scattering 74 Parity 88 Ehrenfest Theorem 95 Quiz 96
CHAPTER 4 An Introduction to State Space 99 Basic Definitions 99 Hilbert Space Definitions 100 Quiz 110
CHAPTER 5 The Mathematical Structure of Quantum Mechanics I 111 Linear Vector Spaces 111 Basis Vectors 122 Expanding a Vector in Terms of a Basis 124 Orthonormal Sets and the Gram-Schmidt Procedure 124 Dirac Algebra with Bras and Kets 125 Finding the Expansion Coefficients in the Representation of Bras and Kets 127 Quiz 129
CHAPTER 6 The Mathematical Structure of Quantum Mechanics II 131 The Representation of an Operator 133 Eigenvalues and Eigenvectors 142 The Hermitian Conjugate of an Operator 152 The Commutator 167 Quiz 172
CHAPTER 7 The Mathematical Structure of Quantum Mechanics III 175 Change of Basis and Unitary Transformations 175 The Generalized Uncertainty Relation 185 Projection Operators 188 Functions of Operators 193 Generalization to Continuous Spaces 194 Quiz 203
CHAPTER 8 The Foundations of Quantum Mechanics 205 The Postulates of Quantum Mechanics 205 Spectral Decomposition 209 Projective Measurements 211 The Completeness Relation 212 Completely Specifying a State with a CSCO 220 The Heisenberg versus Schrödinger Pictures 221 Describing Composite Systems in Quantum Mechanics 222 The Matrix Representation of a Tensor Product 223 The Tensor Product of State Vectors 224 The Density Operator 226 The Density Operator for a Completely Mixed State 229 A Brief Introduction to the Bloch Vector 237 Quiz 239
CHAPTER 9 The Harmonic Oscillator 241 The Solution of the Harmonic Oscillator in the Position Representation 241 The Operator Method for the Harmonic Oscillator 250 Number States of the Harmonic Oscillator 253 More on the Action of the Raising and Lowering Operators 256 Quiz 258
CHAPTER 10 Angular Momentum 259 The Commutation Relations of Angular Momentum 260 The Uncertainty Relations for Angular Momentum 262 Generalized Angular Momentum and the Ladder Operators 262 Matrix Representations of Angular Momentum 272 Coordinate Representation of Orbital Angular Momentum and the Spherical Harmonics 283 Quiz 293
CHAPTER 11 Spin-1/2 Systems 295 The Stern-Gerlach Experiment 296 The Basis States for Spin-1/2 Systems 298 Using the Ladder Operators to Construct Sx, Sy 300 Unitary Transformations for Spin-1/2 Systems 308 The Outer Product Representation of the Spin Operators 310 The Pauli Matrices 312 The Time Evolution of Spin-1/2 States 317 The Density Operator for Spin-1/2 Systems 328 Quiz 329
CHAPTER 12 Quantum Mechanics in Three Dimensions 331 The 2-D Square Well 332 An Overview of a Particle in a Central Potential 341 An Overview of the Hydrogen Atom 342 Quiz 356
Final Exam 357 Answers to Quiz and Exam Questions 363 References 385 Index 387
Quantum Field Theory Demystified
CHAPTER 1 Particle Physics and Special Relativity 1
CHAPTER 2 Lagrangian Field Theory 23
CHAPTER 3 An Introduction to Group Theory 49
CHAPTER 4 Discrete Symmetries and Quantum Numbers 71
CHAPTER 5 The Dirac Equation 85
CHAPTER 6 Scalar Fields 109
CHAPTER 7 The Feynman Rules 139
CHAPTER 8 Quantum Electrodynamics 163
CHAPTER 9 Spontaneous Symmetry Breaking and the Higgs Mechanism 187
CHAPTER 10 Electroweak Theory 209
CHAPTER 11 Path Integrals 233
CHAPTER 12 Supersymmetry 245
Final Exam 263
Solutions to Quizzes and Final Exam 281
References 289
Index 291
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