Physical implications of Fisher-information's scaling symmetry
We study the scaling properties of Fisher's information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher's measure I and encounter that, from the concomitant operati...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2012 |
| Country: | Argentina |
| Institution: | Universidad Nacional de La Plata |
| Repository: | SEDICI (UNLP) |
| Language: | English |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/84298 |
| Online Access: | http://sedici.unlp.edu.ar/handle/10915/84298 |
| Access Level: | Open access |
| Keyword: | Física Fisher Information Legendre structure reciprocity relations scaling transform |
| Summary: | We study the scaling properties of Fisher's information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher's measure I and encounter that, from the concomitant operating rules, several interesting, albeit known, results can be derived. This entails that such results can be regarded as pre-configured by the conjunction of scaling and information theory. The central notion to be arrived at is that scaling entails that I must obey a certain partial differential equation (PDE). These PDE-solutions have properties that enable the application of a Legendre-transform (LT). The conjunction PDE+LT leads one to obtain several quantum results without recourse to the Schrödinger's equation. |
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