### abstract

- The spectrum of a double well constructed of a square barrier embedded in an infinite well is analyzed. Level statistics for levels slightly above the barrier show signs of Wigner statistics usually associated with quantum chaos. The correspondence with Wigner statistics improves when an ensemble of systems with slightly different barrier heights is taken, possibly reflecting an adiabatic time-dependent modulation of the barrier. PACS numbers: 05.45.+b,05.30.Ch,73.40.Gk Typeset using REVTEX 1 One of the most celebrated definitions of classical chaos is the exponential divergence in time of neighboring points in phase space. In discussing the possible existence of quantum chaos, one would like to keep as close as possible to the above definition. Implicitly, one needs to construct a legitimate quantum mechanical paraphrase of the above definition. In fact, the wave function of a particle may be thought of as representing an ensemble of points in phase space while its spread as function of time is a measure of the divergence of those