  By recourse to i) the Hellmann-Feynman theorem and ii) the Virial one, the
information-optimizing principle based on Fisher's information measure uncovers
a Legendre-transform structure associated with Schr\"odinger's equation, in
close analogy with the structure that lies behind the standard thermodynamical
formalism. The present developments provide new evidence for the information
theoretical links based on Fisher's measure that exist between Schr\"odinger's
equation, on the one hand, and thermodynamics/thermostatistics on the other
one.
