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

In this communication we show that Fisher’s information measure emerges as a direct consequence of the scale-invariance of Schroedinger’s equation. Interesting, well-known additional results are re-obtained as well, for whose derivation only (and this is the novelty) the scale invariance property is needed, without further ado.

[1]  Melville S. Green.  Principles of Statistical Mechanics. The Information Theory Approach. Amnon Katz. Freeman, San Francisco, 1967. xii + 188 pp., illus. $8 , 1968 .

[2]  J. Zinn-Justin.  Quantum Field Theory and Critical Phenomena , 2002 .

[3]  B H Soffer,et al.  Fisher-based thermodynamics: its Legendre transform and concavity properties. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  A. R. Plastino,et al.  Legendre-transform structure derived from quantum theorems , 2011, 1101.4661.

[5]  B. Frieden.  Science from Fisher Information , 2004 .

[6]  A. Messiah.  Quantum Mechanics , 1961 .

[7]  David Wallace,et al.  An Introduction To Hellmann-feynman Theory , 2005 .

[8]  P. M. Mathews,et al.  A Textbook of quantum mechanics , 1978 .

[9]  Flavia Pennini,et al.  Localization estimation and global vs. local information measures , 2007 .

[10]  B. Frieden,et al.  Physics from Fisher Information: A Unification , 1998 .

[11]  Walter Greiner,et al.  Quantum Mechanics: An Introduction , 1989 .

[12]  K. Banerjee,et al.  W. K. B. approximation and scaling , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  H. Cramér.  Mathematical methods of statistics , 1947 .

[14]  J. Wheeler.  Information, physics, quantum: the search for links , 1999 .

[15]  A. R. Plastino,et al.  Special features of the relation between Fisher information and Schrödinger eigenvalue equation , 2011 .

[16]  Angelo Plastino,et al.  Fisher information, the Hellmann–Feynman theorem, and the Jaynes reciprocity relations , 2011 .

[17]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[18]  A. R. Plastino,et al.  A conceptual framework for the Wheeler program , 2004 .

[19]  A. Caticha.  Insufficient Reason and Entropy in Quantum Theory , 1998, quant-ph/9810074.

[20]  E. Villaseñor.  Introduction to Quantum Mechanics , 2008, Nature.