Parameter-free ansatz for inferring ground state wave functions of even   potentials
  Schr\"odinger's equation (SE) and the information-optimizing principle based on Fisher's information measure (FIM) are intimately linked, which entails the existence of a Legendre transform structure underlying the SE. In this comunication we show that the existence of such an structure allows, via the virial theorem, for the formulation of a parameter-free ground state's SE-ansatz for a rather large family of potentials. The parameter-free nature of the ansatz derives from the structural information it incorporates through its Legendre properties. 
S. P. Flego, A. Plastino, A. R. Plastino
quant-ph math-ph math.MP