Inferring an optimal Fisher measure

Abstract

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.