Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues

It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-opti- mizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the exis-tence of a Legendre transform structure underlying the SE. Such a structure leads to a...

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Autores principales: Flego, Silvana, Plastino, Ángel Luis, Plastino, Ángel Ricardo
Formato: Articulo
Lenguaje:Inglés
Publicado: 2011
Materias:
Física
Information theory
Fisher’s Information Measure
Legendre Transform
Quartic Anharmonic Oscillator
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/119318
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-119318
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Information theory
Fisher’s Information Measure
Legendre Transform
Quartic Anharmonic Oscillator
spellingShingle Física
Information theory
Fisher’s Information Measure
Legendre Transform
Quartic Anharmonic Oscillator
Flego, Silvana
Plastino, Ángel Luis
Plastino, Ángel Ricardo
Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
topic_facet Física
Information theory
Fisher’s Information Measure
Legendre Transform
Quartic Anharmonic Oscillator
description It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-opti- mizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the exis-tence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial dif-ferential 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 pre-sent procedure does not involve free fitting parameters.
format Articulo
Articulo
author Flego, Silvana
Plastino, Ángel Luis
Plastino, Ángel Ricardo
author_facet Flego, Silvana
Plastino, Ángel Luis
Plastino, Ángel Ricardo
author_sort Flego, Silvana
title Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
title_short Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
title_full Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
title_fullStr Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
title_full_unstemmed Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
title_sort direct fisher inference of the quartic oscillator’s eigenvalues
publishDate 2011
url http://sedici.unlp.edu.ar/handle/10915/119318
work_keys_str_mv AT flegosilvana directfisherinferenceofthequarticoscillatorseigenvalues
AT plastinoangelluis directfisherinferenceofthequarticoscillatorseigenvalues
AT plastinoangelricardo directfisherinferenceofthequarticoscillatorseigenvalues
bdutipo_str Repositorios
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