Parameter-free ansatz for inferring ground state wave functions of even potentials

Abstract

Schrödinger'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.

References in corpus (3)

• Legendre-transform structure derived from quantum theorems
• Inferring an optimal Fisher measure
• Direct Fisher inference of the quartic oscillator's eigenvalues