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Fundamental Concepts
Quantum Mechanics
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Fundamental Concepts
Breakdown of Classical Physics
Photon Polarization
Fundamental Principles of Quantum Mechanics
Ket Space
Bra Space
Operators
Outer Product
Eigenvalues and Eigenvectors
Observables
Measurements
Expectation Values
Degeneracy
Compatible Observables
Uncertainty Relation
Continuous Spectra
Exercises
Position and Momentum
Introduction
Poisson Brackets
Wavefunctions
Schrödinger Representation
Generalized Schrödinger Representation
Momentum Representation
Heisenberg Uncertainty Principle
Displacement Operators
Exercises
Quantum Dynamics
Introduction
Schrödinger Equation of Motion
Heisenberg Equation of Motion
Ehrenfest Theorem
Schrödinger Wave Equation
Charged Particle Motion in Electromagnetic Fields
Gauge Transformations in Electromagnetism
Flux Quantization and the Aharonov-Bohm Effect
Exercises
Orbital Angular Momentum
Orbital Angular Momentum
Eigenvalues of Orbital Angular Momentum
Rotation Operators
Eigenfunctions of Orbital Angular Momentum
Motion in Central Field
Energy Levels of Hydrogen Atom
Exercises
Spin Angular Momentum
Introduction
Properties of Spin Angular Momentum
Wavefunction of Spin One-Half Particle
Rotation Operators in Spin Space
Magnetic Moments
Spin Precession
Pauli Two-Component Formalism
Spinor Rotation Matrices
Factorization of Spinor-Wavefunctions
Spin Greater Than One-Half Systems
Exercises
Addition of Angular Momentum
Introduction
Commutation Rules
Clebsch-Gordon Coefficients
Calculation of Clebsch-Gordon Coefficients
Exercises
Time-Independent Perturbation Theory
Introduction
Two-State System
Non-Degenerate Perturbation Theory
Quadratic Stark Effect
Degenerate Perturbation Theory
Linear Stark Effect
Fine Structure
Zeeman Effect
Hyperfine Structure
Exercises
Time-Dependent Perturbation Theory
Introduction
General Analysis
Two-State System
Nuclear Magnetic Resonance
Dyson Series
Sudden Perturbations
Energy-Shifts and Decay-Widths
Harmonic Perturbations
Absorption and Stimulated Emission of Radiation
Spontaneous Emission of Radiation
Electric Dipole Transitions
Forbidden Transitions
Magnetic Dipole Transitions
Electric Quadrupole Transitions
Photo-Ionization
Exercises
Identical Particles
Introduction
Permutation Symmetry
Spin Statistics Theorem
Two-Electron System
Helium Atom
Orthohelium and Parahelium
Variational Principle
Hydrogen Molecule Ion
Exercises
Scattering Theory
Introduction
Fundamental Equations
Born Approximation
Born Expansion
Partial Waves
Optical Theorem
Determination of Phase-Shifts
Hard-Sphere Scattering
Low-Energy Scattering
Resonant Scattering
Elastic and Inelastic Scattering
Scattering of Identical Particles
Exercises
Relativistic Electron Theory
Introduction
Preliminary Analysis
Dirac Equation
Lorentz Invariance of Dirac Equation
Free Electron Motion
Electron Spin
Motion in Central Field
Fine Structure of Hydrogen Energy Levels
Positron Theory
Exercises
Physical Constants
Bibliography
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Richard Fitzpatrick 2016-01-22
