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1.
E. Witten, Phys. Today 33(7), 3843 (1980).
http://dx.doi.org/10.1063/1.2914163
2.
L. G. Yaffe, Rev. Mod. Phys. 54, 407 (1982).
http://dx.doi.org/10.1103/RevModPhys.54.407
3.
Dimensional Scaling in Chemical Physics, edited by D. R. Herschbach, J. Avery, and O. Goscinski (Kluwer Academic Publishers, London, 1993).
4.
C. T. Tsipis, V. S. Popov, D. R. Herschbach, and J. S. Avery, New Methods in Quantum Theory (Kluwer Academic Publishers, Dordrecht, 1996).
5.
A. Svidzinsky, G. Chen, S. Chin, M. Kim, D. Ma, R. Murawski, A. Sergeev, M. Scully, and D. Herschbach, Int. Rev. Phys. Chem. 27, 665723 (2008).
http://dx.doi.org/10.1080/01442350802364664
6.
A. Chatterjee, Phys. Rep. 186, 249 (1990).
http://dx.doi.org/10.1016/0370-1573(90)90048-7
7.
J. Avery, Hyperspherical Harmonics and Generalized Sturmians (Kluwer, Dordrecht, 2000).
8.
S. H. Dong, Wave Equations in Higher Dimensions (Springer, New York, 2011).
9.
M. Krenn, M. Huber, R. Fickler, R. Lapkiewicz, S. Ramelowa, and A. Zeilinger, Proc. Natl. Acad. Sci. U. S. A. 111, 6243-6247 (2014).
http://dx.doi.org/10.1073/pnas.1402365111
10.
G. Bellomo, A. R. Plastino, and A. Plastino, Int. J. Quantum Inf. 13(6), 1550039 (2015).
http://dx.doi.org/10.1142/S021974991550015X
11.
J. Crann, D. W. Kribs, R. H. Levene, and I. G. Todorov, J. Math. Phys. 57, 015208 (2016).
http://dx.doi.org/10.1063/1.4935399
12.
C. M. Bender, S. Boettcher, and L. R. Mead, J. Math. Phys. 5, 368 (1994).
http://dx.doi.org/10.1063/1.530778
13.
C. M. Bender, S. Boettcher, and M. Moshe, J. Math. Phys. 5, 4941 (1994).
http://dx.doi.org/10.1063/1.530824
14.
A. Beldjenna, J. Rudnick, and G. Gaspari, J. Phys. A 24, 2131 (1991).
http://dx.doi.org/10.1088/0305-4470/24/9/022
15.
C. M. Bender and K. A. Milton, Phys. Rev. D 50, 6547 (1994).
http://dx.doi.org/10.1103/PhysRevD.50.6547
16.
L. G. Yaffe, Phys. Today 36(8), 50 (1983).
http://dx.doi.org/10.1063/1.2915799
17.
D. R. Herschbach, Faraday Discuss. Chem. Soc. 84, 465 (1987).
http://dx.doi.org/10.1039/dc9878400465
18.
D. R. Herschbach, Int. J. Quantum Chem. 57, 295 (1996).
http://dx.doi.org/10.1002/(SICI)1097-461X(1996)57:3<295::AID-QUA3>3.0.CO;2-T
19.
D. R. Herschbach, Annu. Rev. Phys. Chem. 51, 139 (2000).
http://dx.doi.org/10.1146/annurev.physchem.51.1.1
20.
D. R. Herschbach, J. Chem. Phys. 84, 838 (1986).
http://dx.doi.org/10.1063/1.450584
21.
S. Pasternack, Proc. Natl. Acad. Sci. U. S. A. 23, 91 (1938).
http://dx.doi.org/10.1073/pnas.23.2.91
22.
A. Ray, K. Mahata, and P. P. Ray, Am. J. Phys. 56, 462 (1988).
http://dx.doi.org/10.1119/1.15579
23.
G. W. F. Drake and R. A. Swainson, Phys. Rev. A 42, 1123 (1990).
http://dx.doi.org/10.1103/PhysRevA.42.1123
24.
D. Andrae, J. Phys. B: At., Mol. Opt. Phys. 30, 4435 (1997).
http://dx.doi.org/10.1088/0953-4075/30/20/008
25.
V. F. Tarasov, Int. J. Mod. Phys. B 18, 31773184 (2004).
http://dx.doi.org/10.1142/S0217979204026408
26.
A. Guerrero, P. Sanchez-Moreno, and J. S. Dehesa, Phys. Rev. A 84, 042105 (2011).
http://dx.doi.org/10.1103/PhysRevA.84.042105
27.
J. D. Hey, Am. J. Phys. 61, 28 (1993).
http://dx.doi.org/10.1119/1.17405
28.
W. van Assche, R. J. Yáñez, R. González-Férez, and J. S. Dehesa, J. Math. Phys. 41, 6600 (2000).
http://dx.doi.org/10.1063/1.1286984
29.
J. S. Dehesa, S. López-Rosa, P. Sánchez-Moreno, and R. J. Yáñez, Int. J. Appl. Math. Stat. 26, 150162 (2012).
30.
J. S. Dehesa, S. López-Rosa, A. Martínez-Finkelshtein, and R. J. Yáñez, Int. J. Quantum Chem. 110, 15291548 (2010).
http://dx.doi.org/10.1002/qua.22244
31.
S. Zozor, M. Portesi, P. Sanchez-Moreno, and J. S. Dehesa, Phys. Rev. A 83, 052107 (2011).
http://dx.doi.org/10.1103/PhysRevA.83.052107
32.
I. V. Toranzo, S. López-Rosa, R. O. Esquivel, and J. S. Dehesa, J. Phys. A: Math. Theor. 49, 025301 (2016).
http://dx.doi.org/10.1088/1751-8113/49/2/025301
33.
A. I. Aptekarev, J. S. Dehesa, A. Martínez-Finkelshtein, and R. J. Yáñez, J. Phys. A: Math. Theor. 43, 145204 (2010).
http://dx.doi.org/10.1088/1751-8113/43/14/145204
34.
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University Press, New York, 2010).
35.
M. M. Nieto, Am. J. Phys. 47, 1067 (1979).
http://dx.doi.org/10.1119/1.11976
36.
R. J. Yanez, W. van Assche, and J. S. Dehesa, Phys. Rev. A 50, 3065 (1994).
http://dx.doi.org/10.1103/PhysRevA.50.3065
37.
V. Aquilanti, S. Cavalli, and C. Coletti, Chem. Phys. 214, 113 (1997).
http://dx.doi.org/10.1016/S0301-0104(96)00310-2
38.
R. Szmytkowski, Ann. Phys. 524(6-7), 345-352 (2012).
http://dx.doi.org/10.1002/andp.201100330
39.
R. Delbourgo and D. Elliott, J. Math. Phys. 50, 062107 (2009).
http://dx.doi.org/10.1063/1.3141534
40.
U. J. Knottnerus, Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters (J. B. Wolters, Groningen, 1960).
41.
Y. L. Luke, The Special Functions and their Approximations (Academic Press, New York, 1969), Vol. 2.
42.
E. B. Saff and V. Totik, Logarithmic Potentials with External Fields, Grundlehren der Mathematischen Wissenschaften Vol. 316 (Springer-Verlak, Berlin, 1997).
43.
E. H. Kennard, Z. Phys. 44, 326 (1927).
http://dx.doi.org/10.1007/BF01391200
44.
W. Beckner, Proc. Am. Math. Soc. 123, 18971905 (1995).
http://dx.doi.org/10.1090/s0002-9939-1995-1254832-9
45.
P. Sánchez-Moreno, R. González-Férez, and J. S. Dehesa, New J. Phys. 8, 330 (2006).
http://dx.doi.org/10.1088/1367-2630/8/12/330
46.
I. V. Toranzo and J. S. Dehesa, EPL 113, 48003 (2016).
http://dx.doi.org/10.1209/0295-5075/113/48003
47.
S. López-Rosa, I. V. Toranzo, P. Sánchez-Moreno, and J. S. Dehesa, J. Math. Phys. 54, 052109 (2013).
http://dx.doi.org/10.1063/1.4807095
48.
A. I. Aptekarev, J. S. Dehesa, P. Sánchez-Moreno, and D. N. Tulyakov, Contemp. Math. 578, 19-29 (2012).
http://dx.doi.org/10.1090/conm/578/11469
49.
A. I. Aptekarev, D. N. Tulyakov, I. V. Toranzo, and J. S. Dehesa, Eur. Phys. J. B 89, 85 (2016).
http://dx.doi.org/10.1140/epjb/e2016-60860-9
50.
C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x
51.
A. Rényi, Probability Theory (Academy Kiado, Budapest, 1970).
52.
C. Tsallis, J. Stat. Phys. 52, 479 (1988).
http://dx.doi.org/10.1007/BF01016429
53.
S. López-Rosa, J. C. Angulo, J. S. Dehesa, and R. J. Yáñez, Physica A 387, 22432255 (2008);
http://dx.doi.org/10.1016/j.physa.2007.12.005
Erratum, S. López-Rosa, J. C. Angulo, J. S. Dehesa, and R. J. Yáñez, Physica A 387, 4729-4730 (2008).
http://dx.doi.org/10.1016/j.physa.2008.04.005
54.
J. S. Dehesa and F. J. Galvez, Phys. Rev. A 37, 3634 (1988).
http://dx.doi.org/10.1103/PhysRevA.37.3634
55.
J. S. Dehesa, S. López-Rosa, and D. Manzano, in Statistical Complexities: Application to Electronic Structure, edited by K. D. Sen (Springer, Berlin, 2012).
56.
See e.g., J. Spanier, and K. B. Oldham, An Atlas of Functions (Springer-Verlag, Berlin, 1987), see also E. W. Weisstein, A Wolfram Web Resource, http://functions.wolfram.com/GammaBetaErf/Pochhammer/16/02/, 2014.
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/content/aip/journal/jmp/57/8/10.1063/1.4961322
2016-08-19
2016-09-28

Abstract

The radial expectation values of the probability density of a quantum system in position and momentum spaces allow one to describe numerous physical quantities of the system as well as to find generalized Heisenberg-like uncertainty relations and to bound entropic uncertainty measures. It is known that the position and momentum expectation values of the main prototype of the -dimensional Coulomb systems, the -dimensional hydrogenic system, can be expressed in terms of some generalized hypergeometric functions of the type () evaluated at unity with = 2 and = 3, respectively. In this work we determine the position and momentum expectation values in the limit of large for all hydrogenic states from ground to very excited (Rydberg) ones in terms of the spatial dimensionality and the hyperquantum numbers of the state under consideration. This is done by means of two different approaches to calculate the leading term of the special functions and involved in the large limit of the position and momentum quantities. Then, these quantities are used to obtain the generalized Heisenberg-like and logarithmic uncertainty relations, and some upper and lower bounds to the entropic uncertainty measures (Shannon, Rényi, Tsallis) of the -dimensional hydrogenic system.

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