Lecture Notes, Chapter 1

[Griffiths] Chapter 6

[Cohen-Tannoudji] Chapter XI(including Complements A-D)

[Cohen-Tannoudji] Chapter XII

• Time-independent perturbation theory for degenerate states: Diagonalizing perturbations and lifting degeneracies
• Time-independent perturbation theory for nondegenerate states: Energy and wavefunction perturbations through second order
• Degeneracy reconsidered
• Simple examples: Perturbing a two-state system, a simple harmonic oscillator, and a bead on a ring
• The fine structure of hydrogen, revisited: Relativistic and spin-orbital effects
• The hydrogen atom in a magnetic field, revisited: The Zeeman effect
• The hydrogen atom in a electric field: The Stark effect
• Van der Waals interaction between neutral atoms

Lecture Notes, Chapter 1

[Griffiths] Chapter 8

• Form of wave functions in classically allowed and classically forbidden regions
• Handling turning points: Connection formulae
• Tunnelling
• Semiclassical approximation to bound state energies

Lecture Notes, Chapter 2

[Griffiths] Chapter 10

• The Born-Oppenheimer approximation and the rotation and vibration of molecules
• The adiabatic theorem
• Application to spin in a time-varying magnetic field
• Berry’s phase, and the Aharonov-Bohm effect revisited
• Resonant adiabatic transitions and The Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem

Lecture Notes, Chapter 2

[Griffiths] Chapter 9

[Cohen-Tannoudji] Chapter XIII

• General expression for transition probability; Adiabatic theorem revisited
• Sinusoidal perturbations; Transition rate
• Emission and absorption of light; Transition rate due to incoherent light; Fermi’s Golden Rule
• Spontaneous emission; Einstein’s A and B coefficients; How excited states of atoms decay; Laser

Lecture Notes, Chapter 2

[Griffiths] Chapter 11

[Cohen-Tannoudji] Chapter VIII

• Definition of cross-section \(\sigma\); and differential cross section \(\sigma/ \Omega\); General form of scattering solutions to the Schrodinger equation, the definition of scattering amplitude \(f\), and the relation of \(f\) to \(d\sigma/d\Omega\); Optical theorem
• The Born approximation: Derivation of Born approximation to \(f\); Application to scattering from several spherically symmetric potentials, including Yukawa and Coulomb; Scattering from a charge distribution
• Low energy scattering: The method of partial waves; Definition of phase shifts; Relation of scattering amplitude and cross section to phase shifts; Calculation of phase shifts; Behavior at low energies; Scattering length; Bound states at threshold; Ramsauer-Townsend effect; Resonances.

Lecture Notes, Chapter 3

[Sakurai] Chapter 3.4

[Cohen-Tannoudji] Complements EIII and FIV

• Pure and mixed states
• Spin-\(1/2\) density operators
• Partial trace
• Generalized measurements and quantum operations
• Thermal states
• Decoherence

Lecture Notes, Chapter 4

[Griffiths] Chapter 5.1, 5.2

[Cohen-Tannoudji] Chapter XIV

• N-particle systems: Identical particles are indistinguishable
• Exchange operator, symmetrization and antisymmetrization
• Exchange symmetry postulate: Bosons and fermions
• Pauli exclusion principle: Slater determinants; Non-interacting fermions in a common potential well
• Exchange force and a first look at hydrogen molecules and helium atoms

Lecture Notes, Chapter 4

[Griffiths] Chapter 5.3

[Cohen-Tannoudji] Chapter XI Complement F

• Fermions in a box at zero temperature: Density of states; energy; degeneracy pressure
• White dwarf stars: Equation of state at \(T = 0\); Chandrasekhar limit; neutron stars
• Electrons in metals: Periodic potentials; Bloch waves; introduction to band structure; metals vs. insulators

Supplementary notes

[Griffiths] Section 10.2.3 (Aharonov-Bohm effect)

[Cohen-Tannoudji] Chapter VI Complement E

• Canonical quantization
• The classical Hamiltonian for a particle in a static magnetic field
• The Schrodinger equation for a charged particle in a magnetic field, via canonical quantization
• Gauge invariance
• Landau level wave functions. Counting the states in a Landau level
• De Haas-Van Alphen effect
• Integer Quantum Hall Effect: Introduction to the ordinary Hall effect; Quantum mechanical problem of a particle in crossed magnetic and electric fields; Calculation of Hall current due to a single filled Landau level; From this idealized calculation to real systems: The role of impurities.
• The Aharonov-Bohm effect

Lecture Notes, Chapter 5

• Using many two-state systems as a quantum computer
• Grover algorithm
• Simon’s algorithm