Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-03-18
Physics
High Energy Physics
High Energy Physics - Theory
2 pages
Scientific paper
10.1103/PhysRevA.66.014104
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 is novel. 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.
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