Short-wave asymptotics of the information entropy of a circular membrane

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 12, Issue 11, 2002, Pages 2387-2392

  Dehesa, J S ^a   Martinez Finkelshtein A ^a   Sorokin, V N ^a  

^a NONE

Author keywords

Asymptotics; Bessel functions; Information entropies; Two dimensional systems

Indexed keywords

ASYMPTOTIC STABILITY; BESSEL FUNCTIONS; COMPUTATIONAL COMPLEXITY; OSCILLATIONS; PROBABILITY DISTRIBUTIONS;

CIRCULAR MEMBRANES;

ENTROPY;

EID: 0036877056     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127402005935     Document Type: Article

References (16)

1. p-norms and entropy for general orthogonal polynomials," RUSS. Acad. Sci. Sb. Math. 82, 373-395.
2. Beckner, W. [1975] "Inequalities in Fourier analysis," Ann. Math. 102, 159-182.
3. Bialynicki-Birula, J. & Mycielsky, J. [1975] "Uncertainty relations for information theory in wave mechanics," Commun. Math. Phys. 44, 129-132.
4. Buyarov, V. S., López Artés, P., Martínez-Finkelshtein, A. & van Asche, W. [2000] "Information entropy of Gegenbauer polynomials," J. Phys. A: Math. Gen. 33, 6549-6560.
5. Dehesa, J. S., Yáñez, R. J., Aptekarev, A. I. & Buyarov, V. [1998] "Strong asymptotics of Laguerre polynomials and information entropies of two-dimensional harmonic oscillator and one-dimensional Coulomb potentials," J. Math. Phys. 39, 3050-3059.
6. Dehesa, J. S., Martínez-Finkelshtein, A. & Sánchez-Ruiz, J. [2001a] "Quantum information entropies and orthogonal polynomials," J. Comput. Appl. Math. 133, 23-46.
7. Dehesa, J. S., Martínez-Finkelshtein, A. & Sorokin, V. N. [2001b] "Position and momentum information entropies for highly excited states of a Toda-like potential," J. Math. Phys., to appear.
8. Dehesa, J. S., Martínez-Finkelshtein, A. & Sorokin, V. [2001c] "Quantum information entropies for highly-excited states of the single-particle systems with power-type potentials," preprint.
9. Gadre, S. R. & Bendale, R. D. [1985a] "Maximization of atomic information-entropy sum in configuration and momentum spaces," Int. J. Quant. Chem. 28, 311-314.
10. Gadre, S. R., Sears, S. B., Chakravorty, S. J. & Bendale, R. D. [1985b] "Some novel characteristics of atomic information entropies," Phys. Rev. A32, 2602-2606.
11. Gadre, S. R. & Bendale, R. D. [1987] "Rigorous relationships among quantum-mechanical kinetic energy and atomic information entropies: Upper and lower bounds," Phys. Rev. A36, 1932-1935.
12. Jeffrey, A. [1995] Handbook of Mathematical Formulas and Integrals (Academic Press, San Diego, CA).
13. Majernik, V. & Opatrný, T. [1996] "Entropie uncertainty relations for a quantum oscillator," J. Phys. A: Math. Gen. 29, 2187-2197.
14. Sánchez-Ruiz, J. [1997a] "Asymptotic formula for the quantum entropy of position in energy eigenstates," Phys. Lett. A226, 7-13.
15. Sánchez-Ruiz, J. [1997b] "Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates," J. Math. Phys. 38, 5031-5043.
16. Yáñez, R. J., van Assche, W. & Dehesa, J. S. [1994] "Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom," Phys. Rev. A50, 3065-3079.