Fisher Information and Quantum Mechanics
S. P. Flego, A. Plastino, A. R. Plastino
International Research Journal of Pure and Applied Chemistry · pp. 25–54 · Published 15 Nov 2011
10.9734/IRJPAC/2012/777Abstract
A suggestive relation links Fisher' information measure (FIM)Iand Schrödinger equation (SE). The connection is based upon the fact that the constrained minimization of I leads to a SE. This, in turn, is the origin of intriguing relationships between various aspects of SE, on the one hand, and the formalism of statistical mechanics derived from Jaynes's maximum entropy principle (MaxEnt), on the other one. The link entails the existence of a Legendre transform structure underlying the SE, which allows for the emergence of two first-order differential equations that must, respectively, be satisfied by i) the Fisher measure and ii) the SE energy eigenvalues. The complete A) I-solution and B) energy-solution are both obtained bypassing the SE and, furthermore, linked by the Legendre structure.
Cited by 7
Hans De Raedt, Mikhail I. Katsnelson, Kristel Michielsen · Annals of Physics · 2014
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Hans De Raedt, Kristel Michielsen · Frontiers in Physics · 2014
H De Raedt, K Michielsen · Physica Scripta · 2014
A. Arbona, C. Bona, J. Massó · Physica A: Statistical Mechanics and its Applications · 2016
Aparna Saha, Benoy Talukdar, Pranab Sarkar · The European Physical Journal Plus · 2018
Hans De Raedt, Mikhail I. Katsnelson, Dennis Willsch · Annals of Physics · 2019
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