Uncertainty relation for Fisher information of D-dimensional single-particle systems with central potentials

Journal of Mathematical Physics

Volumn 47, Issue 10, 2006, Pages

  Romera, Elvira ^a   Sanchez Moreno P ^a   Dehesa, J S ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750570982     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2357998     Document Type: Article

References (38)

1. W. Heisenberg, Z. Phys. 43, 172 (1927).
2. E. Kennard, Z. Phys. 44, 326 (1927).
3. J. Uffink, " Measures of uncertainty and the uncertainty principle., " (Ph.D. thesis, University of Utrecht, 1990); also see references therein.
4. I. Hirschman, Am. J. Math. 79, 152 (1957).
5. W. Beckner, Ann. Math. 102, 159 (1975).
6. I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975).
7. C. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
8. C. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949).
9. T. Cover and J. Thomas, Elements of Information Theory (Wiley, New York, 1991).
10. R. Fisher, Proc. Cambridge Philos. Soc. 22, 700 (1925), reprinted in collected papers of R. A. Fisher, edited by J. H. Bennet (University of Adelaide Press, South Australia, 1972), pp. 15-40.
11. R. Fisher, Statistical Methods and Scientific Inference, 2nd ed. (Oliver and Boyd, London, 1959).
12. B. Frieden, Science From Fisher Information (Cambridge University Press, Cambridge, 2004).
13. A. Stam, Inform. Control 2, 105 (1959).
14. E. Jaynes, Phys. Rev. 106, 620 (1957).
15. E. Jaynes, Phys. Rev. 108, 171 (1957).
16. S. R. Gadre, Reviews of Modern Quantum Chemistry: A Celebration of the Contributions of Robert G. Parr, edited by, K. D. Sen, (World Scientific, New Jersey, 2002).
17. A. Nagy, J. Chem. Phys. 119, 9401 (2003).
18. S. Sears, R. Parr, and U. Dinur, Isr. J. Chem. 19, 165 (1980).
19. R. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).
20. E. Romera and J. S. Dehesa, Phys. Rev. A 50, 256 (1994).
21. E. Romera and J. S. Dehesa, J. Chem. Phys. 120, 8906 (2004).
22. R. González-F́rez and J. S. Dehesa, Eur. Phys. J. D 32, 39 (2005).
23. J. S. Dehesa, S. López-Rosa, B. Olmos, and R. Yáez, J. Math. Phys. 47, 052104 (2006).
24. E. Romera, J. Angulo, and J. S. Dehesa, Phys. Rev. A 59, 4064 (1999).
25. A. Dembo, T. Cover, and J. Thomas, IEEE Trans. Inf. Theory 37, 1501 (1991).
26. E. Romera, Mol. Phys. 35, 5181 (2002).
27. J. Avery, Hyperspherical Harmonics and Generalized Sturmians (Kluwer, Dordrecht, 2000).
28. A. Chatterjee, Phys. Rep. 186, 249 (1990).
29. J. Louck, J. Mol. Spectrosc. 4, 334 (1960).
30. C. Grosche and F. Steiner, J. Math. Phys. 36, 2354 (1995).
31. C. Grosche and F. Steiner, Handbook of Feynman Path Integrals (Springer-Verlag, Berlin, 1998).
32. E. Romera, P. Sánchez-Moreno, and J. S. Dehesa, Chem. Phys. Lett. 414, 468 (2005).
33. J. S. Dehesa, A. Martinez-Finkelshtein, and V. Sorokin, Mol. Phys. 104, 613 (2006).
34. A. Ray, K. Mahata, and P. Ray, Am. J. Phys. 56, 462 (1998).
35. W. van Assche, R. Yáez, R. González-F́rez, and J. S. Dehesa, J. Math. Phys. 41, 660 (2000).
36. J. S. Dehesa, S. López-Rosa, B. Olmos, and R. Yáez, J. Comput. Appl. Math. 179, 185 (2005).
37. S. Dong and M. Lozada-Cassou, Mod. Phys. Lett. A 20, 1533 (2005).
38. S. Dong, C. Chen, and M. Lozada-Cassou, J. Phys. B 38, 2211 (2005).