By recourse to i) the Hellmann-Feynman theorem and ii) the Virial one, the information-optimizing principle based on Fishers information measure uncovers a Legendre-transform structure associated with Schrodingers 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 Fishers measure that exist between Schrodingers equation, on the one hand, and thermodynamics/thermostatistics on the other one.
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