Georgia Institute of Technology College of Sciences

Given a set in some manifold M, what is the probability that a quantum particle freely traveling in M spends a positive amount of time in the given set? Sets for which there is a positive (uniform) probability after some long time will be called observation sets. We will survey the well-studied case of compact manifolds and discuss our recent extension of these results to the non-compact setting of the whole Euclidean space. This is joint work with Perry Kleinhenz.