Information-theoretic measures of hyperspherical harmonics
- Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071 Granada (Spain) and Departamento de Fisica Moderna, Universidad de Granada, 18071 Granada (Spain)
The multidimensional spreading of the hyperspherical harmonics can be measured in a different and complementary manner by means of the following information-theoretic quantities: the Fisher information, the average density or first-order entropic moment, and the Shannon entropy. They give measures of the volume anisotropy of the eigenfunctions of any central potential in the hyperspace. Contrary to the Fisher information, which is a local measure because of its gradient-functional form, the other two quantities have a global character because they are powerlike (average density) and logarithmic (Shannon's entropy) functionals of the hyperspherical harmonics. In this paper we obtain the explicit expression of the first two measures and a lower bound to the Shannon entropy in terms of the labeling indices of the hyperspherical harmonics.
- OSTI ID:
- 20929685
- Journal Information:
- Journal of Mathematical Physics, Vol. 48, Issue 4; Other Information: DOI: 10.1063/1.2712913; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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