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Constrained energy minimizations of a many-body Hamiltonian return energylandscapes e(b) where b=<B> representes the average value(s) of one (orseveral) collective operator(s), B, in an "optimized" trial state Phi_b, and e= <H> is the average value of the Hamiltonian in this state Phi_b. It isnatural to consider the uncertainty, Delta e, given that Phi_b usually belongsto a restricted set of trial states. However, we demonstrate that theuncertainty, Delta b, must also be considered, acknowledging corrections totheoretical models. We also find a link between fluctuations of collectivecoordinates and convexity properties of energy surfaces.

Fluctuations of collective coordinates and convexity theorems for energy surfaces