Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues

• 作者: A. R. Plastino Angelo Plastino S. P. Flego
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: INFORMATION Theory Fisher’s INFORMATION Measure LEGENDRE Transform QUARTIC ANHARMONIC Oscillator
• 年，卷（期）: 2011,（11）
• 页码范围: 1390-1396
• 页数: 7页
• 分类号: O1

摘要

It is well known that a suggestive connection links Schr?dinger’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 Schr?dinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our present procedure does not involve free fitting parameters.