Quantum Mechanics

Richard Fitzpatrick

Professor of Physics


The University of Texas at Austin

• • Major Sources
  • Purpose of Course
• 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
  • Uncertainty Relation
  • Displacement Operators
  • Exercises
• Quantum Dynamics
  • Schrödinger Equation of Motion
  • Heisenberg Equation of Motion
  • Ehrenfest Theorem
  • Schrödinger Wave Equation
  • 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
  • Spin Greater Than One-Half Systems
  • Exercises
• Addition of Angular Momentum
  • Introduction
  • Analysis
  • 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
  • Spin Magnetic Resonance
  • Dyson Series
  • Sudden Perturbations
  • Energy-Shifts and Decay-Widths
  • Harmonic Perturbations
  • Absorption and Stimulated Emission of Radiation
  • Electric Dipole Approximation
  • Spontaneous Emission
  • Exercises
• Scattering Theory
  • Introduction
  • Fundamental Equations
  • Born Approximation
  • Partial Waves
  • Optical Theorem
  • Determination of Phase-Shifts
  • Hard Sphere Scattering
  • Low Energy Scattering
  • Resonance Scattering
  • Exercises
• Identical Particles
  • Permutation Symmetry
  • Symmetrization Postulate
  • Two-Electron System
  • Helium Atom
  • Exercises
• Relativistic Electron Theory
  • Introduction
  • 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
• About this document ...