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.