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 Schrödinger’s equation, in close analogy with the structure that lies behind the...

A principled framework to generalize variational perturbation approximations (VPAs) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free...