Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates

Journal of Mathematical Physics

Volumn 38, Issue 10, 1997, Pages 5031-5043

  Sánchez Ruiz, Jorge ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040877142     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531931     Document Type: Article

References (30)

1. P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, 864-870 (1964).
2. R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules (Oxford U.P., New York, 1989).
3. E. S. Kryachko and E. V. Ludeña, Density Functional Theory of Many-Electron Systems (Kluwer, Dordrecht, 1989).
4. R. M. Dreizler and E. K. U. Gross, Density Functional Theory: An Approach to the Quantum Mechanics (Springer-Verlag, Heidelberg, 1990).
5. N. H. March, Electron Density Theory of Atoms and Molecules (Academic, New York, 1992).
6. S. R. Gadre and R. D. Bendale, "Rigorous relationships among quantum-mechanical kinetic energy and atomic information entropies: upper and lower bounds," Phys. Rev. A 36, 1932-1935 (1987).
7. J. C. Angulo and J. S. Dehesa, "Tight rigorous bounds to atomic information entropies," J. Chem. Phys. 97, 6485-6495 (1992).
8. J. C. Angulo, "Uncertainty relationships in many-body systems," J. Phys. A 26, 6493-6497 (1993).
9. J. C. Angulo, "Information entropy and uncertainty in D-dimensional many-body systems," Phys. Rev. A 50, 311-313 (1994).
10. R. J. Yáñez, J. C. Angulo, and J. S. Dehesa, "Information entropies of many-electron systems," Int. J. Quantum Chem. 56, 489-498 (1995).
11. W. Beckner, "Inequalities in Fourier analysis," Ann. Math. 102, 159-182 (1975).
12. I. Bialynicki-Birula and J. Mycielski, "Uncertainty relations for information entropy in wave mechanics," Commun. Math. Phys. 44, 129-132 (1975).
13. I. Bialynicki-Birula, "Entropic uncertainty relations," Phys. Lett. A 103, 253-254 (1984).
14. M. Grabowski, "The spreading of free wave packets and the entropy of position," J. Math. Phys. 22, 303-305 (1981).
15. M. Grabowski, "The entropy of position and the spreading of wave packets," Rep. Math. Phys. 24, 327-331 (1986).
16. N. Canosa, A. Plastino, and R. Rossignoli, "Ground-state wave functions and maximum entropy," Phys. Rev. A 40, 519-525 (1989).
17. N. Canosa, R. Rossignoli, and A. Plastino, "Information theory and energy spectra," Phys. Rev. A 43, 1145-1152 (1991).
18. N. Balakrishnan and N. Sathyamurthy, "Maximization of entropy during a chemical reaction," Chem. Phys. Lett. 164, 267-269 (1989).
19. R. J. Yáñez, W. Van Assche, and J. S. Dehesa, "Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom," Phys. Rev. A 50, 3065-3079 (1994).
20. J. S. Dehesa, W. Van Assche, and R. J. Yáñez, "Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator cigenstates," Meth. Appl. Anal. 4, 91-110 (1997).
21. p-norms and entropy for general orthogonal polynomials," Russ. Acad. Sci. Sb. Math. 82, 373-395 (1995).
22. A. I. Aptekarev, J. S. Dehesa, and R. J. Yáñez, "Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials," J. Math. Phys. 35, 4423-4428 (1994).
23. W. Van Assche, R. J. Yáñez, and J. S. Dehesa, "Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential," J. Math. Phys. 36, 4106-4118 (1995).
24. A. I. Aptekarev, V. S. Buyarov, W. Van Assche, and J. S. Dehesa, "Asymptotics of entropy integrals for orthogonal polynomials," Dokl. Math. 53, 47-49 (1996).
25. J. Sánchez-Ruiz, "Asymptotic formula for the quantum entropy of position in energy eigenstates," Phys. Lett. A 226, 7-13 (1997).
26. V. Majerník and T. Opatrný, "Entropic uncertainty relations for a quantum oscillator," J. Phys. A 29, 2187-2197 (1996).
27. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, San Diego, 1994).
28. H. Kleindienst and A. Lüchow, "Multiplication theorems for orthogonal polynomials," Int. J. Quantum Chem. 48, 239-247 (1993).
29. Y. L. Luke, The Special Functions and their Approximations (Academic, New York, 1969), Vol. I.
30. K. M. Case, "Sum rules for zeros of polynomials. I," J. Math. Phys. 21, 702-714 (1980).