| |
| |
| |
| The Origins of Quantum Mechanics | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Blackbody Radiation The Problem with Blackbody Radiation | |
| |
| |
| |
| The Nature of Light The Photoelectric Effect The Compton Effect Is it a Particle or a Wave? | |
| |
| |
| |
| TheWave Nature of Matter | |
| |
| |
| |
| The Bohr Atom | |
| |
| |
| |
| Where do we Stand? | |
| |
| |
| |
| Math Interlude A: Complex Numbers and Linear Operators | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Operators Definition of an Operator Eigenfunctions and Eigenvalues | |
| |
| |
| |
| The Schrodinger Equation | |
| |
| |
| |
| Derivation of the Schrodinger Equation | |
| |
| |
| |
| The Meaning of theWave Function | |
| |
| |
| |
| The Time-Independent Schrodinger Equation Derivation of the Time-Independent Schrodinger Equation Qualitative Solutions and the Origin of Quantization | |
| |
| |
| |
| One-Dimensional Time-Independent Schrodinger Equation | |
| |
| |
| |
| Unbound States: Scattering and Tunneling Scattering From Step-Function Potentials | |
| |
| |
| |
| Bound Systems The Infinite SquareWell The Harmonic Oscillator Potential | |
| |
| |
| |
| Math Interlude B: Linear Algebra | |
| |
| |
| |
| Properties of Linear Operators | |
| |
| |
| |
| Vector Spaces Inner Products Adjoint and Hermitian Operators Basis Sets | |
| |
| |
| |
| The Three-Dimensional Time-Independent Schrodinger Equation | |
| |
| |
| |
| Solution in Rectangular Coordinates | |
| |
| |
| |
| Angular Momentum | |
| |
| |
| |
| The Schrodinger Equation in Spherical Coordinates | |
| |
| |
| |
| The Hydrogen Atom | |
| |
| |
| |
| Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function | |
| |
| |
| |
| The Matrix Formulation of Linear Operators | |
| |
| |
| |
| Dirac Notation | |
| |
| |
| |
| The Dirac Delta Function | |
| |
| |
| |
| Spin Angular Momentum | |
| |
| |
| |
| Spin Operators | |
| |
| |
| |
| Evidence for Spin | |
| |
| |
| |
| Adding Angular Momentum | |
| |
| |
| |
| The Matrix Representation of Spin | |
| |
| |
| |
| The Stern-Gerlach Experiment | |
| |
| |
| |
| Spin Precession | |
| |
| |
| |
| Spin Systems with Two Particles Noninteracting Spins Interacting Spins | |
| |
| |
| |
| Measurement Theory Hidden Variables The Many | |
| |
| |
| Worlds Interpretation of Quantum Mechanics | |
| |
| |
| |
| Time-Independent Perturbation Theory | |
| |
| |
| |
| Derivation of Time-Independent Perturbation Theory | |
| |
| |
| |
| Perturbations to the Atomic Energy Levels Fine Structure The Lamb Shift | |
| |
| |
| |
| The Atom in External Electric or Magnetic Fields The Atom in an Electric Field: The Stark Effect The Atom in a Magnetic Field: The Zeeman Effect | |
| |
| |
| |
| The Variational Principle | |
| |
| |
| |
| Variational Principle: Theory | |
| |
| |
| |
| Variational Principle: Application to the Helium Atom | |
| |
| |
| |
| Time-Dependent Perturbation Theory | |
| |
| |
| |
| Derivation of Time-Dependent Perturbation Theory | |
| |
| |
| |
| Application: Selection Rules for Electromagnetic Radiation | |
| |
| |
| |
| Scattering Theory | |
| |
| |
| |
| Definition of the Cross Section | |
| |
| |
| |
| The Born Approximation | |
| |
| |
| |
| PartialWaves | |
| |
| |
| |
| The Multiparticle Schrodinger Equation | |
| |
| |
| |
| Wave Function for Identical Particles | |
| |
| |
| |
| Multielectron Atoms | |
| |
| |
| |
| Some Modern Applications of Quantum Mechanics | |
| |
| |
| |
| Magnetic Resonance Imaging | |
| |
| |
| |
| Quantum Computing | |
| |
| |
| |
| What Comes Next? Relativistic Quantum Mechanics | |
| |
| |
| |
| The Klein-Gordon Equation Derivation of the Klein-Gordon Equation Probability Densities and Currents | |
| |
| |
| |
| The Dirac Equation | |
| |
| |
| Answers and Hints for Selected | |
| |
| |
| End-of-Chapter Exercises | |
| |
| |
| Index | |