The interesting thing about all of these projects is that I do not know exactly what you will find. You are largely in unknown territory!

1. Stability of 3-Body Systems. Start the earth, Jupiter, sun system with reasonable initial conditions (e.g, circular orbits in a plane as a reasonable approximation, with the right distances and orbital velocities, and ignoring the other planets). Is this system stable? Now increase the mass of Jupiter by factors of 10, 100, and 1000. What happens? Try putting Jupiter near the sun, as in the extra-solar planetary systems which have been discovered only within the past several years. Explore the general stability of a three-body system like this. [See pp. 101-102.]

2. Nightfall with Several Suns. "Nightfall", by Isaac Asimov, has been voted the all-time best science fiction short story. (It has also been made into a low-budget movie.) A planet rotates on its axis at the same time that it revolves in a system with several suns. Night falls only once about every two thousand years. (One of this planet's years is apparently about the same as an earth year.) Create a system that satisfies these conditions. [See pp. 101-102, and buy a paperback with the story in it.]

3. Collision of two galaxies. Let each be a spiral "galaxy" consisting of about a hundred stars, rather than billions. Vary the relative orientation, the angular momenta, and other parameters that occur to you, and see what happens. [See Chapter 9.]

4. Formation of galaxies and larger structures in the universe. According to the modern view, dark matter (consisting of particles that have not yet been identified) acted to seed the formation of galaxies and other structures from ordinary luminous matter. Start a few hundred stars moving (in a plane), together with about the same number of "dark" particles, all having random initial positions and velocities, and try to get "galaxies" to form. The dark particles should have about 10 times the total mass of the luminous particles. What happens if the dark matter is removed? [See Chapter 9.]

5. Is cold fusion possible? Time-independent approach. Take two square wells, each 5 MeV deep and 1 fermi across. (These are respectively a characteristic nuclear energy and a characteristic nuclear size, defined in texbooks. If you like, you can use more precise values relevant to deuterium.) Separate the two wells by 1 Angstrom (a characteristic atomic size, or spacing between deuterium nuclei when absorbed into a solid like palladium). Now place a deuteron in each well. Calculate the ground-state wavefunction for the deuteron on the left, and then use this to calculate the probability that this particle will be found in the well on the right. This is the probability that this nucleus will tunnel through the potential barrier between the nuclei to achieve cold fusion, with deuterium + deuterium fusing to become helium 4. Does cold fusion appear to be a likely process? [See Chapter 10. Meg Ryan's character in the movie "IQ" must have done an analysis something like this. If you want to become a multi-billionaire, win a Nobel Prize, and obtain a place in history, find a way around this problem. This is what another woman scientist is supposed to have done in a less convincing movie, "The Saint".]

6. Is cold fusion possible? Time-dependent approach. Using the same basic model as above, start the deuteron off in a wavefunction that would be the ground-state wavefunction in an infinite square well. Then solve the time-dependent Schroedinger equation, and see what the probability is that the deuteron on the left can tunnel through the barrier, in whatever period of time is feasible without using an inordinate amount of computer time. Does this suggest that cold fusion is a likely process? [See Chapter 10.]

7. Photodissociation of a molecule. Consider the two-atom system near the beginning of the paper at http://prb.aps.org under Volume 58, page 13627. (You can download a pdf file, to read with the free Adobe Acrobat Reader, or a ps file, to print out, if you like. The journal reference is Phys. Rev. B 58, 13627 (1998).) The initial Hamiltonian for this molecule is the 2x2 matrix in Equation (1.1) of this paper. Now add an electromagnetic field by multiplying the original Hamiltonian by a factor which contains a time-dependent vector potential A(t), as in Eq. (3.4) of the paper. There are two electrons, in the ground state, with spin up and spin down. Using the ideas in this paper, such as Eq. (2.5), solve for the electron wavefunction as a function of time, and for the motion of the atomic nuclei. The electron wavefunction is a 2-component vector, and it is obtained from the time-dependent Schrodinger equation. The coordinates of the atomic nuclei are obtained from Newton's second law, F=ma, with F given by the Hellmann-Feynman theorem (2.5). [See also Chapters 9 and 10.]

8. Quantum mechanics of interacting particles. The wavefunction for two particles in one dimension is a function of both coordinates, which may be called x and y. The Hamiltonian for the system is the sum of the one-particle Hamiltonians plus the Coulomb interaction. Solve the time-independent Schrodinger equation for two particles in an infinite square well (or in a harmonic oscillator potential), and plot the wavefunction as a function of x and y. Then plot the wavefunction if you ignore the Coulomb repulsion. [Assume the particles have the same mass, but are distinguishable, so you do not have to worry about symmetrizing or anti-symmetrizing the wavefunction, as is required for real bosons or fermions. See Chapter 10.]

9. Solitons. Simulate the collision of two solitons with each other, or the collision of a soliton with a boundary. See the article by P.S. Lomdahl. [Also see Chapter 6.]

10. Co-evolution of species. Make up rules for how members of various species are born, live, and die, according to the environment that you invent (and may change) and their interaction with the members of other species. Let them randomly mutate, and see if natural selection can be observed. Are there phase transitions in evolution? See Statistical Mechanics, by L. Reichl. [Also see Chapters 7 and 8.]

11. Atomic Chess. Make up rules for how various chemical species of atoms (like Ga and As) interact with each other on a growth surface, and see if you can grow various structures. You can make the atoms move (or diffuse) around on the growth surface while more atoms are being deposited. For example, atoms which are strongly bound to the surface will tend to grow out, whereas atoms that are strongly bound to each other will tend to grow up. If you were growing a metal oxide, each metal atom M wants to bond to an oxygen atom O, and each O to an M. So you could specify that an M-O bond is never broken, but an M-M or O-O bond can be broken. Make up your own rules for some interesting system.

12. Deep impact. Simulate the collision of an asteroid with the Atlantic Ocean, and the motion of the resulting tidal wave as it enters shallow water near the coast. I do not have a clear perception myself of how to set up this problem in a feasible way, so we will have to consult the relevant books and the oceanographers!

13. The Strategic Defense Initiative. A beautiful dream is the idea that a defensive system could provide complete protection against incoming nuclear missiles. Do a reasonably realistic simulation of upgoing missiles attempting to intercept downcoming missiles which are taking evasive action, and see if the possibility of an air-tight defense is believable.

14. Nonlinear systems and chaos. Solve one of the nonlinear problems which exhibit chaos, in Chaos and Fractals, by H.-O.Peitgen et al., or in Introduction to Nonlinear Physics, by L. Lam. Better yet, invent your own nonlinear model which exhibits chaos.

15. The Wide World of Computational Physics. Extend any suitable problem in our textbook, or just make up your own problem.