Upper bounds on Shannon and Renyi entropies for central potentials

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3549585· OSTI ID:21501260

Sanchez-Moreno, P ^[1]; Zozor, S ^[2]; Dehesa, J S ^[3]

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1. Departamento de Matematica Aplicada, Universidad de Granada, Granada (Spain)
2. GIPSA-Lab, Domaine universitaire, 38402 St. Martin d'Heres (France)
3. Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Granada, Granada (Spain)

The Renyi and Shannon entropies are information-theoretic measures, which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation. Moreover, they are closely related to various energetic density functionals of quantum systems. Here we derive upper bounds on these quantities in terms of the second-order moment <r{sup 2}> for general central potentials. This improves previous results of this type. The proof uses the Renyi maximization procedure with a covariance constraint due to Costa et al. [in Proceedings of the Fourth International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), edited by A.Rangarajan, M.A. T.Figueiredo, and J.Zerubia (Springer-Verlag, Lisbon, 2003), [Lect. Notes Comput. Sci. 52, 211 (2003).]] The contributions to these bounds coming from the radial and angular parts of the physical wave functions are taken into account. Finally, the application to the d-dimensional (d{>=} 3) hydrogenic and oscillator-like systems is provided.

• OSTI ID: 21501260
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 2; Other Information: DOI: 10.1063/1.3549585; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CENTRAL POTENTIAL
COMPUTERS
ENTROPY
FUNCTIONALS
HARMONIC OSCILLATORS
INFORMATION THEORY
MEASURE THEORY
MINIMIZATION
OSCILLATORS
PATTERN RECOGNITION
UNCERTAINTY PRINCIPLE
WAVE FUNCTIONS
ELECTRONIC EQUIPMENT
EQUIPMENT
FUNCTIONS
MATHEMATICS
OPTIMIZATION
PHYSICAL PROPERTIES
POTENTIALS
THERMODYNAMIC PROPERTIES