Statistical measures of complexity for quantum systems with continuous variables

The Fisher–Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is shown that evaluating this measure only in the configuration or in the momentum spaces does not provide an adequate characterization of the complexity of some quantum systems. In order to obtain a more complete description of complexity two new measures, respectively based on the minimization and the integration of the usual Fisher–Shannon measure over all the parameter space, are proposed and compared. Finally, these measures are applied to the concrete case of a free particle in a box.