An exactly soluble model of a shallow double well
  Shallow one-dimensional double well potentials appear in atomic and molecular physics and other fields. Unlike the "deep" wells of macroscopic quantum coherent systems, shallow double wells need not present low-lying two-level systems. We argue that this feature, the absence of a low-lying two-level system in certain shallow double wells, may allow the finding of new test grounds for quantum mechanics in mesoscopic systems. We illustrate the above ideas with a family of shallow double wells obtained from Bargman potentials through the Darboux-B\"{a}cklund transform. 
R. Mu\~noz-Vega, E. L\'opez-Ch\'avez, E. Salinas-Hern\'andez, J. J.   Flores-Godoy and G. Fern\'andez-Anaya
quant-ph