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Week 5


See the project information page to start preparing your project proposal. At the end of this lecture I will talk about some numerical approaches to quantum dots. Two topics needed by many students:
  • Solving path problems on phelafel, aluf, t2 and phclasses - download .cshrc to your main directory. Then write source .cshrc
  • Visualization with AViz - scheduled for next weeek.

  • Programs for this week week5.tar and installation instructions. If you take executables from websites remember to write e.g. chmod +x ex2.ex to make it ready to run. Now we will start to cover material from chapter 3 of Koonin, concerning boundary value and eigenvalue problems. This is a continuation of the discussion on differential equations, delving into some special cases in detail.

    We will view videos of solutions of Schroedinger equations and mpegs of these can be downloaded from the psa site.

    For a cute comparison we can view Molecular Dynamics used to simulate vibrations in nanotubes, see: here.

    Finally we will look at five different numerical approaches to Scroedinger equations:

    1. A useful website (php) way to get energy levels, recommended for Modern Physics teachers and metargelim. See Yaron Artzi's project
    2. The Schroedinger equation for the Hydrogen atom has an exact solution so we can use this to visualize the electronic density.
      First project - Joey Fox
      Second project - Meital Krief
    3. There are numerical approaches to use various approximations to solve Schroedinger equations: See Or Cohen's project.
    4. Some ``canned'' codes to do this are installed on TAMNUN. One of the best is Quantum Espresso, and some of you use VASP. I will give an introduction to Quantum Espresso near the end of the course.
    5. There is a ready MATLAB interpretation of the quantum well model, see Dany Regelman's project.
    6. There is also an old fortran/MATLAB quantum well project by Aleksandra Milovanovich from 1998 which can be accessed here. It is the time dependent SE, but worth trying out for those who want projects in this direction. In those days, programs went on an ftp server called phjoan12 (backed up now on the web in http://phjoan23.technion.ac.il/~phr76ja/old_pub and I wrote the html.

    Aleks', Yaron's and Dany's projects are from the class, the other final undergrad or intern projects.

    We will continue with the time dependent SE after we do partial differential equations.

    QUANTUM DOTS: The Scroedinger equation with a well is one way to model Quantum Dots. Another is to model one in Molecular Dynamics - see Yahel's project. MD is next week's topic! Back to the index page


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    Technion - Israel Institute of Technology

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