  We seek for the optimal strategy to infer the width $a$ of an infinite
potential wells by performing measurements on the particle(s) contained in the
well. In particular, we address quantum estimation theory as the proper
framework to formulate the problem and find the optimal quantum measurement, as
well as to evaluate the ultimate bounds to precision. Our results show that in
a static framework the best strategy is to measure position on a delocalized
particle, corresponding to a width-independent quantum signal-to-noise ratio
(QSNR), which increases with delocalisation. Upon considering time-evolution
inside the well, we find that QSNR increases as $t^2$. On the other hand, it
decreases with $a$ and thus time-evolution is a metrological resource only when
the width is not too large compared to the available time evolution. Finally,
we consider entangled probes placed into the well and observe super-additivity
of the QSNR: it is the sum of the single-particle QSNRs, plus a positive
definite term, which depends on their preparation and may increase with the
number of entangled particles. Overall, entanglement represents a resource for
the precise characterization of potential wells.
