Bound states in bottomless potentials

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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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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