Physics 404 - Quantum Physics III - Spring 2002

Welcome to the Physics 404 WWW pages!

The motivation for this course is to teach some fundamental aspects of quantum mechanics and, in particular, to illustrate their relevance and applications to major areas of physics including condensed matter, optical, molecular, nuclear, and particle physics.

A syllabus is given below:

Photon Physics   (Cooke)

[Jan. 16- Feb. 6]

Although the concept of a photon – a quantized unit of electromagnetic energy – was crucial for the creation of quantum mechanics, we have often relegated it to a minor role simply explaining the photo-electric effect.  This section of  PHYS 404 will begin by laying a formal foundation for second quantization, which quantizes electromagnetic fields to produce photons.  From there, we will show how the photon itself simplifies a wide variety of calculations that drive current optical research.

  1. Second Quantization:
    Quantizing the electromagnetic vector potential introduces creation and annihilation operators.
  2. Relativistic Photons:
    The particle nature of a photon makes it easy to transform electromagnetic fields.
  3. Lasers:
    Stimulated emission is a fundamental quantum effect that leads to optical gain.
  4. Photon Interactions:
    The concept of a photon cross-section is surprisingly general and extremely useful.
  5. Cooling and Trapping with photons:
    One of the most active areas of atomic physics uses laser to cool and trap atoms.  We will discuss some of the clever mechanisms, such as Doppler cooling and Sisyphus cooling, and some of the best current traps (e.g. the MOT).
  6. Nonlinear Optics:
    Conservation rules for photon energy and momenta easily explain most nonlinear optical phenomena.

Spectroscopy and NMR   (Hoatson)

[Feb. 8 - Mar. 1]

Spectroscopy refers to the interaction of electromagnetic radiation with matter, and provides many beautiful examples of quantum mechanical principles. Quantized (bound) states are obtained by solving the time-independent Schrödinger equation in absence of radiation, and the probability of radiation-induced transitions among these states is obtained by solving the time dependent Schroödinger equation. Statistical mechanics is needed to extend this formalism to the interaction of radiation with condensed matter, and to account for effects of phase coherent radiation. This series of lectures will develop these principles and illustrate them with specific examples taken from Nuclear Magnetic Resonance (NMR). NMR provides particularly clear examples of the general quantum mechanical formalism, and the results indicate how useful information about condensed matter systems can be obtained. Topics to be covered include:

  1. General Spectroscopy:
    Regions of the electromagnetic spectrum and the physical phenomena responsible for spectroscopy. Classification of bound states, stimulated and spontaneous emission.
  2. Quantum Mechanics of Angular Momentum:
    Matrix representation of angular momentum operators, commutation relations, exponential operators and rotations in Hilbert space.
  3. Time Independent Schrödinger Equation:
    Hamiltonian operator, eigenvalues (energies) and eigenfunctions (state vectors) for nuclear spins interacting with each other and with a static magnetic field. Exact solution of the appropriate Schrödinger equation will be obtained and compared with results of perturbation theory.
  4. Density Matrix Theory:
    Wavefunction expansion coefficients and how they relate to observables. Ensemble averages, eigenstate populations, and coherent superpositions of eigenstates. Illustrative examples include ensembles of spin 1/2 and spin 1 particles.
  5. Time Evolution:
    Phase coherence, the free induction decay signal and the NMR spectrum. Spin echoes and analogies with optical quantum beats and photon echoes.
  6. Multiple Quantum Coherence:
    How to measure "forbidden" multiple quantum phase coherence, and why this is useful. Effective Hamiltonian operators, indirect detection and two dimensional Fourier transformation.

Nuclear Physics   (Griffioen)

[Mar. 11 - Apr. 3]

  1. The Deuteron:
  2. Nuclear Shell Model:
  3. Nuclear alpha-decay:
    phenomenology, barrier tunneling, WKB approximation.

Particle Physics   (Armstrong)

[Apr. 5 - Apr. 26]

Particle physics is the study of the fundamental particles in nature and their interactions. Elementary particles are intrinisically quantum-mechanical objects, and so they exhibit many properties that can only be understood via quantum mechanics. We will study a selected number of these phenomena that highlight various features of quantum mechanics, including interference and superposition, field quantization, and new symmetries, and we will introduce some areas of current research.

  1. Introduction to Particle Physics:
    Fundamental Forces, the classification of particles (fermions, bosons, leptons, hadrons, baryons, mesons, etc.)
  2. Fundamental Symmetries and new Quantum Numbers:
    Noether's theorem, parity, isospin, flavor, color, time-reversal, etc.
  3. Survey of Elementary Particle Dynamics
  4. Scattering and Partial Wave Analysis:
  5. Hadron Spectroscopy and the Quark Model:
    angular momentum coupling, selection rules, 'exotic' particles, charmonium, etc.
  6. The neutral Kaon system:
    interferences, basis states, CP violation, CPT.

College of William and Mary,
Dept. of Physics

armd@physics.wm.edu
last updated: Jan. 7 2002