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arXiv · 1106.2078

Direct Fisher inference of the quartic oscillator's eigenvalues

S. P. Flego·A. Plastino·A. R. Plastino
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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. As an application we deal with the quantum theory of anharmonic oscillators, a long-standing problem that has 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 particular PDE-solution that yields the 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.

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S. P. Flego, A. Plastino, A. R. Plastino. 2011-06-22. Direct Fisher inference of the quartic oscillator's eigenvalues. https://doi.org/10.4236/jmp.2011.211171

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