A closed, quantum, double barrier, GaAs/AlGaAs heterostructure is considered, and the dynamical behavior of an electron cloud moving in the heterostructure is examined. The motion of the electron cloud is represented by a mean field approximation, thus we have a representation of a nondissipative system which mixes in some region of its phase space, showing some chaotic characteristics. With the addition of the potential term &agr;⟨Q(t)⟩, the nonlinear, time‐dependent Schro¨dinger equation is solved for the amount of charge trapped in the heterostructure. As the nonlinear parameter &agr; increases, we find a tenfold increase in the Lyapunov exponent which provides a quantitative measure of the chaos inherent in the system. The phase space plots, autocorrelation function, and power spectrum are also discussed as a function of &agr;. ©1996 American Institute of Physics.