Bound states in bottomless potentials

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number1
StatePublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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