Timeindependent perturbation theory

Lecture Notes, Chapter 1
[Griffiths] Chapter 6
[CohenTannoudji] Chapter XI(including Complements AD)
[CohenTannoudji] Chapter XII

 Timeindependent perturbation theory for degenerate states: Diagonalizing perturbations and lifting degeneracies
 Timeindependent perturbation theory for nondegenerate states: Energy and wavefunction perturbations through second order
 Degeneracy reconsidered
 Simple examples: Perturbing a twostate system, a simple harmonic oscillator, and a bead on a ring
 The fine structure of hydrogen, revisited: Relativistic and spinorbital 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

The Semiclassical (or WKB) approximation

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

The adiabatic approximation and Berry’s phase

Lecture Notes, Chapter 2
[Griffiths] Chapter 10

 The BornOppenheimer approximation and the rotation and vibration of molecules
 The adiabatic theorem
 Application to spin in a timevarying magnetic field
 Berry’s phase, and the AharonovBohm effect revisited
 Resonant adiabatic transitions and The MikheyevSmirnovWolfenstein solution to the solar neutrino problem

Timedependent perturbation theory

Lecture Notes, Chapter 2
[Griffiths] Chapter 9
[CohenTannoudji] 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

Scattering

Lecture Notes, Chapter 2
[Griffiths] Chapter 11
[CohenTannoudji] Chapter VIII

 Definition of crosssection \(\sigma\); 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; RamsauerTownsend effect; Resonances.

Density Operators

Lecture Notes, Chapter 3
[Sakurai] Chapter 3.4
[CohenTannoudji] Complements EIII and FIV

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

Introduction to the quantum mechanics of identical particles

Lecture Notes, Chapter 4
[Griffiths] Chapter 5.1, 5.2
[CohenTannoudji] Chapter XIV

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

Degenerate Fermi systems

Lecture Notes, Chapter 4
[Griffiths] Chapter 5.3
[CohenTannoudji] 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

Charged particles in a magnetic field

Supplementary notes
[Griffiths] Section 10.2.3 (AharonovBohm effect)
[CohenTannoudji] 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 HaasVan 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 AharonovBohm effect

Quantum Computing and quantum information

Lecture Notes, Chapter 5

 Using many twostate systems as a quantum computer
 Grover algorithm
 Simon’s algorithm
