Phys. Rev. A 66, 014104 (2002) [2 pages]Bound states in bottomless potentialsReceived 1 April 2002; published 24 July 2002 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. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.66.014104
DOI:
10.1103/PhysRevA.66.014104
PACS:
03.65.Ge
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