Research is a vitally important part of physics education. I maintain a program of research problems that a bright undergraduate student can tackle and which are directly relevant for theoretical physics. This is both a learning process and a research discovery process for the student.
In addition, the UConn Physics Department hosts undergraduate students from all around the U.S.A. during the summer months as part of the National Science Foundation's R.E.U. program - Research Experience for Undergraduates.
I have collaborated with two undergraduate students recently through this program.
Periodic Superpotentials in Quantum Mechanical Supersymmetry
Jake Mannix, from U. C. Santa Cruz, worked with me on supersymmetry breaking in systems with periodic superpotentials. We showed that supersymmetry breaking can occur with periodic superpotentials, but that the sensitivity to the parameters in the superpotential is more acute than for conventional non-periodic cases. This work was published in Physics Letters B428 (1998) 115, and a preprint version is available from the Cornell archive.
Numerical method for computing tunneling ionization rates for arbitrary potentials
Kyle Bergquist, from Wake Forest, worked with George Gibson (a laser experimentalist in our department) and me on a simple new way to calculate tunneling ionization rates for systems where the tunneling involves multiple (and arbitrarily shaped) barriers. This is directly relevant to the ionization of molecules in strong laser fields, and is also a good example of spectral analysis in quantum mechanics. This work was published in Physical Review Letters 81 (1998) 2663, and a preprint version is available from the Cornell archive.
An exactly soluble molecular ionization model
Chris Gauthier, a UConn undergraduate, has done some research with me in mathematical and atomic physics, finding an exact solution to a one-dimensional molecular ionization problem where the molecule is represented by a pair of delta function wells and the applied electrostatic field is represented by a linear potential. Such a problem cannot be studied using perturbation theory for a strong electric field, as is the case in modern studies of atoms and molecules in intense lasers. This work was published in Physical Review A 69 (2004) 053049. A preprint version of this work can be found at Simple Soluble Molecular Ionization Model, and see here for some animations of the spectral function. This work forms the basis for Chris Gauthier's 2003/2004 UConn Senior Thesis, which was awarded the UConn Physics Department's Katzenstein Prize for best undergraduate research, and was nominated for the American Physical Society's Apker Award for the best Undergraduate Senior Thesis.