Information Theory Consequences of the Scale-Invariance of Schröedinger’s Equation

Flego, Silvana; Plastino, A.; Plastino, A.

doi:10.3390/e13122049

Cited by 3 publications

(9 citation statements)

References 17 publications

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“…This, in turn, implies intriguing relationships between various aspects of SWE, on the one hand, and the formalism of statistical mechanics as derived from Jaynes's maximum entropy principle, on the other one. In particular, fundamental consequences of the SWE, such as the Hellmann-Feynman and Virial theorems, can be re-interpreted in terms of a special kind of reciprocity relations between relevant physical quantities similar to the ones exhibited by the thermodynamics' formalism [4,5]. This demonstrates that a Legendre-transform structure underlies the nonrelativistic Schrödinger equation.…”

Section: Introductionmentioning

confidence: 85%

“…Some useful results of Refs. [4,5] will be needed below. An essential ingredient in the present considerations is the virial theorem [18] that, of course, applies in this Schrödinger-scenario [19].…”

Section: Basic Ideasmentioning

confidence: 99%

“…Eq. (14) encodes the information provided by the virial theorem [4,5]. Note that if we define M−dimensional vectors X of…”

Section: Basic Ideasmentioning

confidence: 99%

“…It is well-known that a strong link exists between Fisher' information measure (FIM) I and Schrödinger wave equation (SWE) [1][2][3][4][5]. In a nutshell, this connection is based upon the fact that the constrained minimization of I leads to a SWE [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…In a nutshell, this connection is based upon the fact that the constrained minimization of I leads to a SWE [1][2][3][4][5]. This, in turn, implies intriguing relationships between various aspects of SWE, on the one hand, and the formalism of statistical mechanics as derived from Jaynes's maximum entropy principle, on the other one.…”

Section: Introductionmentioning

confidence: 99%

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

Flego

Plastino

2011

Journal of Mathematical Physics

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It is well known that a suggestive relation exists that links Schrödinger'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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Section: Introductionmentioning

confidence: 85%