We consider classical and quantum dynamics on potentials that are asymptotically unbounded from below. By explicit construction we find that quantum bound states can exist in certain bottomless potentials. The classical dynamics in these potentials has the property that only a set of zero measure of classical trajectories can escape to infinity. All other trajectories get trapped as they get further out into the asymptotic region.
|Number of pages
|Physical Review A - Atomic, Molecular, and Optical Physics
|Published - 2002
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics