584 Computational Methods

Tentative Syllabus

Mark Alford (Jan 26, Feb 2)

Mathematica for Statistical Mechanics of Fermions

Requirements: Before starting the class, students should

• Make sure you have easy access to Mathematica. Preferably it should be installed on your own laptop.
  • Physics graduate students: for a free Mathematica license, write to Sai Iyer giving your WUSTL email address and approximate month and year of graduation.
  • Undergraduates (and non-physics grads): buy it for $25.00 from Software Licensing. Send email to WU_SoftwareLicensing@wumail.wustl.edu giving your first and last name, Washington University email address, and how payment will be made (check or credit/debit card). Once payment has been satisfied you will receive a unique activation code.
• Reproduce all the examples in my Introduction to Mathematica
• Study (and preferably reproduce) the examples in my Mathematica Techniques
• Refresh your undergraduate statistical mechanics knowledge. Make sure you understand the following:
  • Pauli exclusion principle
  • Fermi Surface
  • Fermi-Dirac distribution

Project: Students should bring their laptop, with Mathematica installed, to class. The following files should be loaded on the laptop:

• First project file containing the exercises that will be explained and that students will start solving in the first class.
• Second project file containing the exercises that will be explained and that students will start solving in the second class.

Wim Dickhoff (Feb 9, 16)

• Project: diagonalization of quantum mechanical potentials.

The Schroedinger equation of Quantum Mechanics can in some cases be solved analytically for discrete eigenvalues and corresponding wave functions. This is true for potentials with spherical symmetry like the Coulomb or 3-D Harmonic Oscillator. We will extend the solution for discrete eigenvalues for bound states of potentials that do not allow an analytical solution.

Francesc Ferrer (Feb 23, Mar 2)

Python/Matplotlib

• Requirements:
  • Make sure that you bring to class your computer with a working Python environment (including Numpy, Scipy and Matplotlib). Consider for example the Enthought distribution, which is available for free and provides a one-click Python installation for Windows, Linux and Mac.
  • Our first goal will be to write a script that produces the bifurcation diagram for the tent-map. To develop the script, and to get used to the language itself, it will be very useful to run Python interactively. It is highly recommended that you use Ipython for this purpose. You can think of Ipython as an equivalent to the Mathematica FrontEnd containing an integrated graphics environment, easily accessible help, and many other useful features. You can launch the shell from the command line ('ipython --pylab' loads the graphics environment automatically), which is faster, or use its web-based notebook environment.

• Background:
  • Some good resources to get acquainted with the basics of the language are listed in the official Python site: Tutorials. An accessible, yet fairly complete, one can be found here; if you have a little bit of programming experience, you might want to browse Google's Python class.
  • Matplotlib will allow you to plot functions and it provides the source code for an extensive list of examples.

Mike Ogilvie (Mar 16, 23)

Project: Our goal is to learn to use Monte Carlo simulation to understand the behavior of complex systems. We will study the two-dimensional Ising model, perhaps the most celebrated model in all theoretical physics.

Background: Introductory material on the Ising model can be found in most graduate-level statistical mechanics texts, as well as [here: http://en.wikipedia.org/wiki/Ising_model Ising model]. The Metropolis algorithm will be covered in detail in class.

Requirements: We will continue with Python and the iPython environment. I will send you via email a working Ising model simulation as an iPython notebook, which you can modify and extend.

Things to do:

• Verify the phase structure is approximately correct
  • Examine the effect of lattice size and run time
  • Examine the difference between a hot start and cold start
  • Preliminary plot of magnetization versus beta
• Determine magnetization as a function of beta
  • Determine an appropriate lattice size and run time
  • Determine equilibration time
  • Explore different ways to measure magnetization
• Advanced topics
  • Susceptibility and specific heat measurements
  • Autocorrelation and statistical error

Erik Henriksen (Mar 30, Apr 6)

• Labview.
• Project: controlling a lab device, and reading data from it.

Kasey Wagoner (Apr 13, 20)

• SolidWorks
• Project: designing a 3D object.