Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues

• Autores: Flego, Silvana; Plastino, Ángel Luis; Plastino, Ángel Ricardo
• Año de publicación: 2011
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Física; Information theory; Fisher’s Information Measure; Legendre Transform; Quartic Anharmonic Oscillator
• Institución: Universidad Nacional de La Plata

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.
Instituto de Física La Plata
Facultad de Ingeniería
Centro Regional de Estudios Genómicos