Lecture 3 homework:

1. [1-2 points each] Mathematical exercises.  Due by 2pm Fri. Feb. 8.  Do any of the exercises &/or problems in chapter 2 of Nielsen & Chuang (one of the course textbooks).  Exercises 2.1, 2.2, 2.4, 2.5, 2.6, 2.7, 2.9, 2.11, 2.12, 2.15, 2.19, 2.26, 2.27, 2.36, 2.38, 2.40, 2.42, 2.44, 2.46, 2.51, 2.52, 2.53 are worth 1 point each; the others are worth 2 points each.
2. Programming projects.  My Schroedinger equation simulator that I showed in class can be found at http://www.cise.ufl.edu/~mpf/sch/, for C and X windows, along with some Java versions (of both 1-D and 2-D simulations) developed by a student.  There are a number of possible projects that would extend this work in various ways:
• (a) [10 points] Play around with and experiment with one or more versions of the simulation.  Experiment with a few different shapes of potential-energy functions and initial wavefunctions, including some new ones not already programmed into the simulation.  What interesting behaviors did you observe?  Write a report on your results.
• (b) [20 points] Write a nice GUI for one of the 1-D versions, that allows the user to twiddle with various parameters of the simulation, draw inital wavefunctions and potential energy functions using the mouse, stop & reverse the simulation, see values of various observables (energy, momentum, etc.), etc.
• (c) [30 points] Like (a), but for the 2-D version.  Also, optimize the code to try to make the simulation as fast as possible.
• (d) [40 points] Write a 3-D version, that renders wavefunction voxels as a transparent colored fog.  Allow the user to move their viewpoint around and through the image.  Atomic orbitals would make for nice initial states.
3. [100 points] Original analytical research.  Extend Motter's proof of the numerical stability of the reversible simulation algorithm (see the above webpage) to cover cases where the potential energy surface is not flat.
4. [7 points] Short paper.  In lecture, I went through a lot of concepts & definitions fairly quickly.  For your short paper, you might pick one or two slides' worth of material that you had trouble understanding, read up on it in more detail using the suggested readings from the reading list page, and write your 2+ page report explaining it in more depth.