Computer Modeling of Charmonium

My current research project is to model charmonium. Charmonium, like positronium, is the bound state to a particle and its antiparticle. In this case, the particle is a charm quark and the antiparticle is the anti-charm quark. These two particles are attracted to each other, and therefore orbit around their common center of mass. Because we can't ever see a lone quark, we see the combination of these two quarks as a meson. Just as a hydrogen atom has a ground state and several excited states, so may the charmonium bound state have a ground state and several excited states. In the case of hydrogen, the level splitting is on the order of a few electron volts (eV, the energy an electron gains when accelerated across a potential of one volt). For charmonium, however, the level splitting is on the order of hundreds of millions of eV, or hundreds of MeV. Because the level splitting is so large, we tend to think of the excited states as different particles. Thus the charmonium spectrum forms the psi family of particles.

In order to predict the masses of the psi family of particles, I am modeling the charmonium spectrum on a computer. Specifically, I am attempting to find the energy eigenvalues corresponding to the ground and excited states of charmonium. This is done by numerically solving the Schrodinger equation, a second-order partial differential equation. The results must then be interpreted, and compared to the experimental data.