Measuring localization-delocalization phenomena in a quantum corral

The standard deviations and Shannon information entropies of the probability densities for a particle in a quantum corral are compared and contrasted to determine their effectiveness in measuring particle (de)localization. We illustrate how the two measures emphasize different aspects of the underlying distributions which can lead to inconsistent interpretations. Among these, we show that the Shannon entropy is able to distinguish between the presence of an attractive or repulsive effective potential in the radial Schrodinger equation while the standard deviation does not. The analysis of this radial model is then extended to momentum space where the dependence of the measures, entropic sum and uncertainty product on the effective potential, is examined.