| dc.creator | Plastino, Ángel Luis | |
| dc.creator | Bellomo, Guido | |
| dc.creator | Plastino, Ángel Ricardo | |
| dc.date | 2015 | |
| dc.date | 2019-11-20T12:31:58Z | |
| dc.identifier | http://sedici.unlp.edu.ar/handle/10915/85739 | |
| dc.identifier | issn:1687-9120 | |
| dc.description | Fisher's information measure I plays a very important role in diverse areas of theoretical physics. The associated measures I<SUB>x</SUB> and I<SUB>p</SUB>, as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product I<SUB>x</SUB>I<SUB>p</SUB> has been conjectured to exhibit a nontrivial lower bound in Hall (2000). More explicitly, this conjecture says that for any pure state of a particle in one dimension I<SUB>x</SUB>I<SUB>p</SUB> ≥ 4. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schrödinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schrödinger equation. We also conjecture that any normalizable time-dependent solution of this equation verifies I<SUB>x</SUB>I<SUB>p</SUB> → 0 for t → ∞. | |
| dc.description | Facultad de Ciencias Exactas | |
| dc.description | Instituto de Física La Plata | |
| dc.format | application/pdf | |
| dc.language | en | |
| dc.rights | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.rights | Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) | |
| dc.subject | Ciencias Exactas | |
| dc.subject | Entropy | |
| dc.subject | Fisher information | |
| dc.subject | Complexity | |
| dc.title | On a conjecture regarding Fisher information | |
| dc.type | Articulo | |
| dc.type | Articulo | |
