This project is research in mathematical physics. Professor Herbst will investigate certain problems connected with Schroedinger operators. (These operators encode the dynamics of quantum mechanical systems. The spectrum of the Schroedinger operator is the set of possible energy levels of the system.) Determining which potentials for the Schroedinger operator in the N-body problem give eigenvalues embedded in the continuous spectrum, and showing that normal exponential decay is generic in this setting are two lines of investigation to be pursued. In addition Professor Herbst hopes to prove a correlation inequality involving Gaussian probabilities and to investigate the question of when a stopping time is a hitting time in the Brownian motion process.
