Position-momentum uncertainty relations based on moments of arbitrary order

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 83, Issue 5, 2011, Pages

  Zozor, Steeve ^a   Portesi, Mariela ^b   Sanchez Moreno, Pablo ^c   Dehesa, Jesus S ^c  

^a CNRS   (France)

^b INSTITUTO DE FÍSICA LA PLATA   (Argentina)

^c UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY ORDER; D-DIMENSIONAL QUANTUM SYSTEMS; HEISENBERG; LOWER BOUNDS; UNCERTAINTY PRINCIPLES; UNCERTAINTY RELATION;

QUANTUM OPTICS;

QUANTUM ELECTRONICS;

EID: 79961047742     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.83.052107     Document Type: Article

References (63)

1. W. C. Price, The Uncertainty Principle and Foundations of Quantum Mechanics, edited by, W. C. Price, and, S. S. Chissick, (Wiley, New York, 1977).
2. Sixty-Two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics, edited by, A. I. Miller, (Plenum, New York, 1990).
3. Dimensional Scaling in Chemical Physics, edited by, D. R. Herschbach, J. Avery, and, O. Goscinski, (Springer-Verlag, New York, 2001).
4. E. H. Lieb, The Stability of Matter: From Atoms to Stars, Selecta of E. H. Lieb, edited by, W. Thirring, (Springer-Verlag, Berlin, 2005).
5. J. S. Dehesa, S. López-Rosa, and D. Manzano, in Statistical Complexities: Application to Electronic Structure, edited by, K. D. Sen, (Springer, Berlin, 2010).
6. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
7. V. Vedral, Introduction to Quantum Information Science (Oxford University Press, Oxford, 2006).
8. W. Heisenberg, Z. Phys. A 1434-6001 10.1007/BF01397280 43, 172 (1927).
9. E. H. Kennard, Z. Phys. EPJAFV 1434-6001 10.1007/BF01391200 44, 326 (1927).
10. G. B. Folland and A. Sitaram, J. Fourier Anal. Appl. EPJAFV 1069-5869 10.1007/BF02649110 3, 207 (1997).
11. P. Busch, T. Heinonen, and P. Lahti, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2007.05.006 452, 155 (2007).
12. I. Bialynicki-Birula and L. Rudnicki, e-print arXiv: 1001.4668.
13. D. Deutsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.631 50, 631 (1983).
14. J. B. M. Uffink and J. Hilgevoord, Found. Phys. FNDPA4 0015-9018 10.1007/BF00739034 15, 925 (1985).
15. J. B. M. Uffink, Ph.D. thesis, University of Utrecht, Utrecht, The Netherlands (1990), see also references therein.
16. J. Hilgevoord and J. B. M. Uffink, in Proceedings of the International Conference on Microphysical Reality and Quantum Description, edited by, F. Selleri, A. van der Merwe, and, G. Tarozzi, (Reidel, Dordrecht, 1988), Vol. 1, pp. 91-114.
17. I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608825 44, 129 (1975).
18. I. Bialynicki-Birula, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74. 052101 74, 052101 (2006). (Pubitemid 44674157)
19. S. Zozor and C. Vignat, Physica A PHYADX 0378-4371 10.1016/j.physa.2006. 09.019 375, 499 (2007). (Pubitemid 44894759)
20. S. Zozor, M. Portesi, and C. Vignat, Physica A PHYADX 0378-4371 10.1016/j.physa.2008.04.010 387, 4800 (2008).
21. A. K. Rajagopal, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95) 00500-3 205, 32 (1995).
22. M. Portesi and A. Plastino, Physica A 0378-4371 10.1016/0378-4371(95) 00475-0 225, 412 (1996).
23. H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.1103 60, 1103 (1988).
24. E. Romera, P. Sánchez-Moreno, and J. S. Dehesa, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2357998 47, 103504 (2006). (Pubitemid 44673078)
25. P. Sánchez-Moreno, R. González-Férez, and J. S. Dehesa, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/12/330 8, 330 (2006). (Pubitemid 46013225)
26. P. Sánchez-Moreno, A. R. Plastino, and J. S. Dehesa, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/44/6/065301 44, 065301 (2011).
27. S. Wehner and A. Winter, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/2/025009 12, 025009 (2010).
28. J. C. Angulo, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/26/22/042 26, 6493 (1993).
29. J. C. Angulo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.50.311 50, 311 (1994).
30. D. V. Widder, The Laplace Transform, Princeton Mathematical Series (Princeton University Press, Princeton, NJ, 1946).
31. E. Romera, J. C. Angulo, and J. S. Dehesa, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.4064 59, 4064 (1999).
32. Y. A. Wang and E. A. Carter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.4153 60, 4153 (1999).
33. R. López-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95)00867-5 209, 321 (1995).
34. S. López-Rosa, J. C. Angulo, and J. Antolín, Physica A PHYADX 0378-4371 10.1016/j.physa.2009.01.037 388, 2081 (2009).
35. S. López-Rosa, R. O. Esquievel, J. C. Angulo, J. Antolín, J. S. Dehesa, and N. Flores-Gallegos, J. Chem. Theor. Comput. PHYADX 1549-9618 10.1021/ct900544m 6, 145 (2010).
36. J. S. Dehesa, S. López-Rosa, A. Martínez-Finkelshtein, and R. J. Yáñez, Int. J. Quantum Chem. 110, 1529 (2010).
37. A. Rényi, in Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, edited by, J. Neyman, Vol. 1 (University of California Press, Berkeley, 1961), pp. 547-561.
38. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
39. J. A. Costa, A. O. Hero III, and C. Vignat, in 4th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Lecture Notes in Computer Sciences, edited by, A. Rangarajan, M. A. T. Figueiredo, and, J. Zerubia, (Springer-Verlag, Lisbon, 2003), Vol. 2683, pp. 211-226.
40. E. H. Lieb, Inventiones Mathematicae INVMBH 0020-9910 10.1007/BF01233426 102, 179 (1990).
41. J. C. Angulo and J. S. Dehesa, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.463710 97, 6485 (1992).
42. S. Nadarajah, J. Appl. Stat. JCPSA6 0266-4763 10.1080/02664760500079464 32, 685 (2005). (Pubitemid 41576633)
43. M. K. Varanasi and B. Aazhang, J. Acoust. Soc. Am. JASMAN 0001-4966 10.1121/1.398700 86, 1404 (1989).
44. S. Zozor and C. Vignat, IEEE Trans. Signal Proc. ITPRED 1053-587X 10.1109/TSP.2009.2030840 58, 134 (2010).
45. R. J. Yáñez, W. Van Assche, R. González-Férez, and J. Sánchez-Dehesa, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.533051 40, 5675 (1999).
46. J. S. Avery, Hyperspherical Harmonics and Generalized Sturmians (Kluwer Academic, Dordrecht, 2002).
47. R. J. Yáñez, W. Van Assche, and J. S. Dehesa, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.50.3065 50, 3065 (1994).
48. R. Lord, Biometrika 0006-3444 10.1093/biomet/41.1-2.44 41, 44 (1954).
49. J. S. Avery, J. Comput. Appl. Math. JCAMDI 0377-0427 10.1016/j.cam.2009. 02.057 233, 1366 (2010).
50. W. Van Assche, R. J. Yáñez, R. González-Férez, and J. S. Dehesa, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1286984 41, 6600 (2000).
51. V. F. Tarasov, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/ S0217979204026408 18, 3177 (2004).
52. A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2: Special Functions (Gordon and Breach Science Publishers, New York, 1986).
53. J. D. Louck and W. H. Shaffer, J. Mol. Spectrosc. JMOSA3 0022-2852 10.1016/0022-2852(60)90091-6 4, 298 (1960).
54. J. D. Louck and W. H. Shaffer, J. Mol. Spectrosc. JMOSA3 0022-2852 10.1016/0022-2852(60)90092-8 4, 334 (1960).
55. J. S. Dehesa, F. J. Galvez, and I. Porras, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.35 40, 35 (1989).
56. C. Tsallis, R. M. Mendes, and A. R. Plastino, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98)00437-3 261, 534 (1998).
57. A. Andai, J. Multivariate Anal. JMVAAI 0047-259X 10.1016/j.jmva.2008.08. 007 100, 777 (2009).
58. S. Kotz and S. Nadarajah, Stat. Prob. Lett. JMVAAI 0167-7152 10.1016/S0167-7152(01)00039-6 54, 171 (2001). (Pubitemid 33619090)
59. Y. Kano, J. Multivariate Anal. JMVAAI 0047-259X 10.1006/jmva.1994.1054 51, 139 (1994).
60. T. J. Kozubowski, Statistics JMVAAI 0233-1888 10.1080/02331880212858 36, 219 (2002). (Pubitemid 36325111)
61. C. Tsallis and E. K. Lenzi, Chem. Phys. CMPHC2 0301-0104 10.1016/S0301-0104(02)00557-8 284, 341 (2002).
62. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, San Diego, 2007).
63. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1970).