Special features of the relation between Fisher information and Schrodinger eigenvalue equation

S.P.FLEGO; A. PLASTINO; A.R.PLASTINO

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2011 vol. 52 p. 821031 - 8210313

0022-2488

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. 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 the 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.