  It is well known that a suggestive relation exists that links Schr\"odinger's
equation (SE) to the information-optimizing principle based on Fisher's
information measure (FIM). We explore here an approach that will allow one to
infer the optimal FIM compatible with a given amount of prior information
without explicitly solving first the associated SE. This technique is based on
the virial theorem and it provides analytic solutions for the physically
relevant FIM, that which is minimal subject to the constraints posed by the
prior information.
