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

TL;DR

This paper introduces a parameter-free approach to approximate ground state wave functions for even potentials by leveraging the Legendre transform structure of Schrödinger's equation and Fisher information, simplifying the process without adjustable parameters.

Contribution

It presents a novel, parameter-free ansatz for ground state wave functions based on the Legendre transform structure linked to Fisher information and the virial theorem.

Findings

The ansatz successfully approximates ground states for a broad class of potentials.

It eliminates the need for adjustable parameters in ground state calculations.

The approach is grounded in the structural properties of Schrödinger's equation and Fisher information.

Abstract

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.