Quantum Mechanics
Syllabus for Quantum Mechanics

Main Texts:

Other useful texts:

Week 1: Brief Mathematical Review (Liboff: Ch. 1 and Secs. 4.3 & 11.2, also Boas if you can find a copy)

  1. Coordinate systems
  2. Ordinary Differential Equations
  3. Complex numbers, integration, and Cauchy's theorem
  4. Notational conventions - Dirac's Bra-ket notation
  5. Matrices, vectors, eigenvalues, eigenvectors, determinants, and traces

Week 2: The Schrödinger Equation (McQuarrie: Chapter 3)

  1. Time-dependent
  2. Time-independent
  3. Linear Operators
  4. Particle in a one-dimensional box

Week 3: Postulates & Theorems (Liboff: Chapters 3 & 4)

  1. The state of the system is given by the wavefunction.
  2. Observables in Classical Mechanics correspond to operators in QM.
  3. QM observables will be measured at the eigenvalues of the operators.
  4. Averages of Quantum observables are obtained from expectation values.
  5. Time-dependence is derived from time-dependent Schrödinger equation.
  6. QM operators are linear, Hermitian operators.
  7. Eigenfunctions of Hermitian operators are orthogonal.
  8. Many operators to not commute.
  9. The Schwarz inequality and the uncertainty principle.

Week 4: The Harmonic Oscillator (Liboff: 7.2, 7.3, Baym: pp. 123-128)

  1. Differential Equations
  2. Raising & Lowering operators
  3. Applications to Spectroscopy

Week 5: Angular momentum (Liboff: Sections 9.1, 9.2, 9.3, Baym: Chapter 6)

  1. Seperability
  2. The Laplacian in Spherical Coordinates
  3. The Rigid Rotator
  4. Spherical Harmonics
  5. Commutation of Angular Momentum operators

Week 6: The Hydrogen Atom (Baym: Chapter 7, Liboff: Sections 10.5, 10.6)

  1. Radial functions
  2. Angular functions
  3. High-Z hydrogenic atoms

Weeks 7 & 8: Approximate Methods (Baym: Chapter 11, McQuarrie: Sections 7.4-7.7, Liboff: Chapter 13)

  1. Perturbation Theory
      a. Derivation of the Van der Waals Interaction
  2. The Variational Method

Weeks 9 & 10: Quantum Scattering (Liboff: Sections 7.5, 7.6, 7.7, 7.10)

  1. Transmission through Potential Steps & Barriers
  2. Airy functions & the WKB Approximation

Weeks 11 & 12: Quantum Statistical Mechanics (Liboff: Chapter 11)

  1. Partition Functions
  2. The Density Matrix