S. P. Flego, B. R. Frieden, A. Plastino, A. R. Plastino and B. H. Soffer, “Non-Equilibrium Thermodynamics and Fisher Information: Sound Waves Propagation in a Dilute Gas,” Physical Review E, Vol. 68, No. 16, 2003, pp. 105- 115.

has been cited by the following article:

• TITLE: Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues

  AUTHORS: S. P. Flego, Angelo Plastino, A. R. Plastino

  KEYWORDS: Information Theory, Fisher’s Information Measure, Legendre Transform, Quartic Anharmonic Oscillator

  JOURNAL NAME: Journal of Modern Physics, Vol.2 No.11, November 24, 2011

  ABSTRACT: It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schrödinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.