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

Physica Scripta (Impact Factor: 1.03). 07/2011; 85(5). DOI: 10.1088/0031-8949/85/05/055002
Source: arXiv

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.

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    01/1979; Dover Publications.
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    ABSTRACT: It is well known that a suggestive relation exists that links Schr\"odinger's equation (SE) to the information-optimizing principle based on Fisher's information measure (FIM). We explore here an approach that will allow one to infer the optimal FIM compatible with a given amount of prior information without explicitly solving first the associated SE. This technique is based on the virial theorem and it provides analytic solutions for the physically relevant FIM, that which is minimal subject to the constraints posed by the prior information.
    Physica A: Statistical Mechanics and its Applications 01/2011; 390(23). · 1.68 Impact Factor
  • 01/1989: pages 366; Springer-Verlag.

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