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Bound quantum states with no classical turning points

Physical Review A, ISSN: 1050-2947, Vol: 52, Issue: 5, Page: 4255-4258
1995
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For a two-parameter class of local potentials which support a bound state with energy E1 embedded in the continuous spectrum, we determine the conditions that the potential has m wells with barriers of height greater than E1. Although E1V()=0, such wells act as traps for a classical particle, with classical turning points wherever a barrier height reaches the energy of the particle. However, the parameters of the potential may easily be chosen so that there are no classical turning points, even though the potential supports a bound quantum state. © 1995 The American Physical Society.

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