Mathematical Sciences: Topics in Mathematical Physics
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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.
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