Special features of the relation between Fisher Information and Schrödinger eigenvalue equation

Details Special features of the relation between Fisher Information and Schrödinger eigenvalue equation Special features of the relation between Fisher Information and Schrödinger eigenvalue equation

2011-05-25

arxiv.org/abs/1105.5054v1

Physics

Quantum Physics

Scientific paper

It is well known that a suggestive relation exists that links Schr\"odinger's equation (SE) to the information-optimizing principle based on Fisher's information measure (FIM). The connection entails the existence of a Legendre transform structure underlying the SE. Here we show that appeal to this structure leads to a first order differential equation for the SE's eigenvalues that, in certain cases, can be used to obtain the eigenvalues without explicitly solving SE. Complying with the above mentioned equation constitutes a necessary condition to be satisfied by an energy eigenvalue. We show that the general solution is unique.

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