Quantum Mechanics


A graduate level course

Richard Fitzpatrick

Associate Professor of Physics

The University of Texas at Austin



  • Introduction
    • Major sources
  • Fundamental concepts
    • The breakdown of classical physics
    • The polarization of photons
    • The fundamental principles of quantum mechanics
    • Ket space
    • Bra space
    • Operators
    • The outer product
    • Eigenvalues and eigenvectors
    • Observables
    • Measurements
    • Expectation values
    • Degeneracy
    • Compatible observables
    • The uncertainty relation
    • Continuous spectra
  • Position and momentum
    • Introduction
    • Poisson brackets
    • Wave-functions
    • Schrödinger’s representation – I
    • Schrödinger’s representation – II
    • The momentum representation
    • The uncertainty relation
    • Displacement operators
  • Quantum dynamics
    • Schrödinger’s equations of motion
    • Heisenberg’s equations of motion
    • Ehrenfest’s theorem
    • Schrödinger’s wave-equation
  • Angular momentum
    • Orbital angular momentum
    • Eigenvalues of angular momentum
    • Rotation operators
    • Eigenfunctions of orbital angular momentum
    • Motion in a central field
    • Energy levels of the hydrogen atom
    • Spin angular momentum
    • Wave-function of a spin one-half particle
    • Rotation operators in spin space
    • Magnetic moments
    • Spin precession
    • Pauli two-component formalism
    • Spin greater than one-half systems
    • Addition of angular momentum
  • Approximation methods
    • Introduction
    • The two-state system
    • Non-degenerate perturbation theory
    • The quadratic Stark effect
    • Degenerate perturbation theory
    • The linear Stark effect
    • Fine structure
    • The Zeeman effect
    • Time-dependent perturbation theory
    • The two-state system
    • Spin magnetic resonance
    • The Dyson series
    • Constant perturbations
    • Harmonic perturbations
    • Absorption and stimulated emission of radiation
    • The electric dipole approximation
    • Energy-shifts and decay-widths
  • Scattering theory


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