Cramér–Rao, Fisher–Shannon and LMC–Rényi Complexity-like Measures of Multidimensional Hydrogenic Systems with Application to Rydberg States

Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydr...

Full description

Saved in:
Bibliographic Details
Published inQuantum reports Vol. 5; no. 1; pp. 116 - 137
Main Author Dehesa, Jesús S.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2023
Subjects
Charged particles
Chemical reactions
Complexity
Cramér–Rao complexity-like measures
Entropy
Fermions
First principles
Fisher–Shannon complexity-like measures
Fourier transforms
highly excited Rydberg states
Hypergeometric functions
LMC–Rényi complexity-like measures
Mathematical analysis
multidimensional hydrogenic systems
Polynomials
Rydberg states
Online AccessGet full text

Cover

Abstract Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by means of the monotone complexity measures of Cramér–Rao, Fisher–Shannon and LMC(Lopez-Ruiz, Mancini, Calbet)–Rényi types. These quantities are shown to be analytically determined from first principles, i.e., explicitly in terms of the space dimensionality D, the nuclear charge and the hyperquantum numbers, which characterize the system’ states. Then, they are applied to several relevant classes of particular states with emphasis on the quasi-spherical and the highly excited Rydberg states, obtaining compact and physically transparent expressions. This is possible because of the use of powerful techniques of approximation theory and orthogonal polynomials, asymptotics and generalized hypergeometric functions.
AbstractList Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the internal disorder of atoms and molecules to the information–theoretical analysis of chemical reactions. This potential will be shown in hydrogenic systems by means of the monotone complexity measures of Cramér–Rao, Fisher–Shannon and LMC(Lopez-Ruiz, Mancini, Calbet)–Rényi types. These quantities are shown to be analytically determined from first principles, i.e., explicitly in terms of the space dimensionality D, the nuclear charge and the hyperquantum numbers, which characterize the system’ states. Then, they are applied to several relevant classes of particular states with emphasis on the quasi-spherical and the highly excited Rydberg states, obtaining compact and physically transparent expressions. This is possible because of the use of powerful techniques of approximation theory and orthogonal polynomials, asymptotics and generalized hypergeometric functions.
Author Dehesa, Jesús S.
Author_xml – sequence: 1
  givenname: Jesús S.
  orcidid: 0000-0003-4397-9426
  surname: Dehesa
  fullname: Dehesa, Jesús S.
BookMark eNpVkc9u1DAQxiNUJErplbMlrqSMnXWyPlYRpZV2VakLErdoYk92vSRxajuC3HiHPkWfo2_CkzTLIgSn-ffT941mXicnvespSd5yuMgyBR_uR-zj2EngAKBeJKciF4tU5fD15J_8VXIewn4mxBKEypenyUPpsXt69L9-Ptyhe8-ubNjRodrssJ89GPaGrdblYf702E-Wla4bWvph45S29huxNWEYPQXmGrYe22iN7agP1vXYsuvJeLel3mq2mUKkLrDvNu7Y5TC0VmOcKRYdu5tMTX7LNhEjhTfJywbbQOd_4lny5erj5_I6Xd1-uikvV6nORKFSRbQomrqQQoMEyVEuF5AbIcEACp5ndaOUBiVq0BIIG4Q8l0RS1qKpJWVnyc1R1zjcV4O3Hfqpcmir3w3ntxX6aHVLFTdSa8VFYcgsailRqqLmUHBVSIClmbXeHbUG7-5HCrHau9HPJwjVvCvPlRIim6mLI6W9C8FT89eVQ3X4Y_X_H7NncTKZew
CitedBy_id crossref_primary_10_1063_5_0153747
crossref_primary_10_1088_1751_8121_ad33da
Cites_doi 10.1016/j.aop.2004.01.002
10.1016/j.cplett.2018.12.032
10.1039/b927055h
10.1007/978-90-481-3890-6
10.1119/1.15579
10.1088/1751-8121/ac3320
10.1016/j.physa.2009.04.023
10.1088/1361-6455/abcdee
10.1016/j.cplett.2009.04.061
10.1016/j.physleta.2007.07.077
10.1007/BF00641720
10.1016/j.physleta.2015.10.047
10.1103/PhysRevE.66.011102
10.1070/SM1995v082n02ABEH003571
10.1007/978-3-319-99639-4
10.1007/BF01608825
10.1016/j.aop.2015.01.031
10.1209/0295-5075/113/48003
10.1063/1.530861
10.1002/qua.24219
10.1063/1.2712913
10.1016/S0375-9601(03)00570-X
10.1002/qua.26424
10.1002/qua.26192
10.3390/sym13081416
10.1016/j.physleta.2008.10.027
10.1080/09500340008244048
10.1103/PhysRevA.59.2602
10.1103/PhysRevA.74.052101
10.1063/1.1286984
10.3390/e19010016
10.1063/1.3141534
10.1063/1.4807095
10.1103/PhysRevA.106.L021101
10.1002/qua.26077
10.1002/qua.26816
10.1063/1.2907743
10.1007/978-1-4471-6464-7
10.1063/1.533051
10.1063/1.2190335
10.1016/j.physa.2009.08.007
10.1063/1.1695600
10.1103/PRXQuantum.3.030340
10.1063/1.5055299
10.1080/01442350110075926
10.1137/S1064827503426711
10.1016/j.cam.2005.03.025
10.1063/1.2357998
10.1016/j.physa.2016.06.144
10.1140/epjst/e2018-00092-4
10.1063/1.3274387
10.1140/epjd/e2014-50127-2
10.1088/1751-8113/40/8/011
10.1007/978-94-011-1836-1
10.1063/1.4986518
10.1017/S0305004100009580
10.1103/PhysRevLett.113.140401
10.1088/1751-8113/45/22/225303
10.1063/1.532238
10.1016/j.physa.2004.03.087
10.1016/B978-0-12-411544-6.00005-4
10.1063/1.5006191
10.3390/e15104084
10.1088/1751-8121/aa95f4
10.1103/PhysRevA.83.052107
10.3390/e19090493
10.1088/1751-8121/abd269
10.1002/qua.26858
10.1016/j.physa.2008.04.010
10.1063/1.2263710
10.1088/1751-8113/44/6/065301
10.1016/j.physa.2011.02.020
10.1103/PhysRevA.84.042105
10.1088/0305-4470/32/42/308
10.1016/S0375-9601(96)00756-6
10.1002/qua.22244
10.1016/j.cam.2009.02.056
10.3390/e24111590
10.1016/j.cplett.2017.09.036
10.1016/S0377-0427(00)00633-6
10.1214/07-AOS539
10.1063/1.532679
10.1016/j.amc.2013.07.076
10.1142/6107
10.1140/epjd/e2009-00251-1
10.1063/1.5006569
10.1002/qua.21832
10.1088/2058-9565/aca996
10.1103/PhysRevA.101.042511
10.1017/CBO9780511616907
10.1016/j.physa.2009.01.037
10.1007/s10910-019-01039-8
10.1088/1742-5468/aacf0c
10.1088/1742-5468/aa6a22
10.1016/j.bpc.2004.12.035
10.1006/jath.1998.3315
10.1063/1.1697374
10.1016/j.physleta.2007.02.028
10.1016/j.aml.2012.01.038
10.1109/18.104312
10.1103/PhysRevE.59.1459
10.1016/0375-9601(95)00867-5
10.1088/1742-5468/aa7df4
10.1016/j.cplett.2005.08.032
10.1002/0470010827
ContentType Journal Article
Copyright 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
8FE
8FG
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
P5Z
P62
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
DOA
DOI 10.3390/quantum5010009
DatabaseName CrossRef
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
AUTh Library subscriptions: ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection (Proquest) (PQ_SDU_P3)
Advanced Technologies & Aerospace Database
ProQuest Advanced Technologies & Aerospace Collection
Access via ProQuest (Open Access)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Advanced Technologies & Aerospace Collection
Technology Collection
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest One Academic
DatabaseTitleList
CrossRef
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: DOA
  name: Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
EISSN 2624-960X
EndPage 137
ExternalDocumentID oai_doaj_org_article_1d5cc9127ded4b55a597b1071975008d
10_3390_quantum5010009
GroupedDBID AADQD
AAYXX
AFKRA
AFZYC
ALMA_UNASSIGNED_HOLDINGS
ARAPS
ARCSS
BENPR
BGLVJ
CCPQU
CITATION
GROUPED_DOAJ
HCIFZ
IAO
IGS
ITC
MODMG
M~E
OK1
PIMPY
8FE
8FG
ABUWG
AZQEC
DWQXO
P62
PQEST
PQQKQ
PQUKI
PRINS
ID FETCH-LOGICAL-c3279-9ee47fb752c05051a58406d250d0a2163bf99c092b0c50eafa0665ee55b2fb5e3
IEDL.DBID DOA
ISSN 2624-960X
IngestDate Tue Oct 22 15:11:19 EDT 2024
Mon Oct 21 07:53:07 EDT 2024
Thu Sep 26 18:40:40 EDT 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c3279-9ee47fb752c05051a58406d250d0a2163bf99c092b0c50eafa0665ee55b2fb5e3
ORCID 0000-0003-4397-9426
OpenAccessLink https://doaj.org/article/1d5cc9127ded4b55a597b1071975008d
PQID 2791699223
PQPubID 5046865
PageCount 22
ParticipantIDs doaj_primary_oai_doaj_org_article_1d5cc9127ded4b55a597b1071975008d
proquest_journals_2791699223
crossref_primary_10_3390_quantum5010009
PublicationCentury 2000
PublicationDate 20230201
PublicationDateYYYYMMDD 2023-02-01
PublicationDate_xml – month: 02
  year: 2023
  text: 20230201
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Quantum reports
PublicationYear 2023
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References ref_92
Toranzo (ref_17) 2017; 2017
ref_91
Hall (ref_75) 1999; 59
Toranzo (ref_107) 2018; 227
Dehesa (ref_95) 2021; 54
Baumgratz (ref_6) 2014; 113
Vignat (ref_10) 2003; 312
Angulo (ref_20) 2014; 68
Majumdar (ref_42) 2017; 687
Mukherjee (ref_43) 2019; 57
Aquino (ref_45) 2020; 120
Romera (ref_19) 2008; 372
Dehesa (ref_60) 2001; 133
ref_22
ref_21
ref_121
Majumdar (ref_44) 2019; 716
Toranzo (ref_74) 2017; 58
Yamano (ref_86) 2004; 45
ref_123
Neyman (ref_71) 1961; Volume 1
Delbourgo (ref_100) 2009; 50
ref_28
Li (ref_34) 2007; 366
ref_26
Aquilanti (ref_33) 2001; 20
Dehesa (ref_97) 2006; 47
Dembo (ref_88) 1991; 37
ref_72
ref_70
Leonenko (ref_78) 2008; 36
Angulo (ref_27) 2009; 388
Dehesa (ref_65) 2006; 186
Dehesa (ref_102) 2007; 40
Sobrino (ref_64) 2022; 122
ref_79
Dehesa (ref_110) 2009; 55
Mycielski (ref_118) 1975; 44
Nagy (ref_13) 2009; 50
ref_77
Rudnicki (ref_7) 2016; 380
Toranzo (ref_111) 2016; 113
Guerrero (ref_89) 2011; 84
Toranzo (ref_23) 2017; 2017
Zozor (ref_84) 2011; 83
Dehesa (ref_30) 2012; 26
Toranzo (ref_112) 2016; 462
Dehesa (ref_105) 2007; 48
Temme (ref_122) 2017; 58
Sen (ref_101) 2006; 125
Buyarov (ref_104) 2004; 26
Aptekarev (ref_113) 2021; 54
Romera (ref_96) 2006; 47
Dehesa (ref_50) 2009; 388
Ray (ref_94) 1988; 56
Dehesa (ref_55) 2013; 223
Zozor (ref_83) 2008; 387
Burgbacher (ref_35) 1999; 40
Rudnicki (ref_119) 2012; 45
Srivastava (ref_58) 1988; 150
Dehesa (ref_106) 1999; 40
Dehesa (ref_117) 1998; 39
(ref_82) 2006; 74
Toranzo (ref_24) 2017; 50
Toranzo (ref_41) 2013; 54
Jizba (ref_81) 2015; 355
Antolin (ref_14) 2009; 474
Catalan (ref_15) 2002; 66
Aptekarev (ref_114) 1994; 35
Sen (ref_2) 2002; Volume 1
Esquivel (ref_51) 2010; 12
Jiao (ref_73) 2017; 58
Vidal (ref_5) 2000; 47
Dehesa (ref_4) 2010; 110
ref_59
Toranzo (ref_103) 2020; 120
Fisher (ref_66) 1925; 22
Romera (ref_12) 2004; 120
Dehesa (ref_54) 1999; 32
Yamano (ref_87) 2004; 340
Coletti (ref_93) 2013; 67
Aptekarev (ref_115) 1995; 82
Manzano (ref_29) 2009; 388
ref_69
ref_67
Esquivel (ref_53) 2013; 15
ref_62
Dehesa (ref_76) 2012; 25
Romera (ref_68) 2005; 414
Buyarov (ref_120) 1999; 99
Anteneodo (ref_40) 1996; 223
Toranzo (ref_56) 2018; 2018
Romera (ref_18) 2009; 3
Dehesa (ref_90) 1994; 50
Dehesa (ref_63) 2021; 54
Aquino (ref_46) 2021; 121
Dehesa (ref_57) 2018; 59
Nath (ref_47) 2022; 122
ref_36
Bouvrie (ref_49) 2011; 390
Esquivel (ref_52) 2012; 112
ref_32
ref_31
Adkins (ref_99) 2020; 101
ref_38
ref_37
ref_108
Plastino (ref_85) 2011; 44
ref_109
Angulo (ref_8) 2009; 109
Aptekarev (ref_61) 2010; 233
Aptekarev (ref_116) 1996; 53
Jizba (ref_80) 2004; 312
(ref_16) 2005; 115
ref_1
ref_3
Angulo (ref_9) 2008; 128
Angulo (ref_11) 2000; 372
Mancini (ref_39) 1995; 209
ref_48
Shiner (ref_25) 1999; 59
Dehesa (ref_98) 2000; 41
References_xml – volume: 312
  start-page: 17
  year: 2004
  ident: ref_80
  article-title: The world according to Rényi: Thermodynamics of multifractal systems
  publication-title: Ann. Phys.
  doi: 10.1016/j.aop.2004.01.002
  contributor:
    fullname: Jizba
– volume: 716
  start-page: 257
  year: 2019
  ident: ref_44
  article-title: Information entropy and complexity measure in generalized Kratzer potential
  publication-title: Chem. Phys. Lett.
  doi: 10.1016/j.cplett.2018.12.032
  contributor:
    fullname: Majumdar
– volume: 12
  start-page: 7108
  year: 2010
  ident: ref_51
  article-title: Analysis of complexity measures and information planes of selected molecules in position and momentum spaces
  publication-title: Phys. Chem. Chem. Phys.
  doi: 10.1039/b927055h
  contributor:
    fullname: Esquivel
– ident: ref_79
  doi: 10.1007/978-90-481-3890-6
– volume: 56
  start-page: 462
  year: 1988
  ident: ref_94
  article-title: Moments of probability distribution, wavefunctions and their derivatives at the origin of N-dimensional central potentials
  publication-title: Am. J. Phys.
  doi: 10.1119/1.15579
  contributor:
    fullname: Ray
– volume: 54
  start-page: 495001
  year: 2021
  ident: ref_63
  article-title: Complexity-like properties and parameter asymptotics of Lq-norms of Laguerre and Gegenbauer polynomials
  publication-title: J. Phys. A Math. Theor.
  doi: 10.1088/1751-8121/ac3320
  contributor:
    fullname: Dehesa
– volume: 388
  start-page: 3273
  year: 2009
  ident: ref_29
  article-title: Complexity of D-dimensional hydrogenic systems in position and momentum spaces
  publication-title: Phys. A
  doi: 10.1016/j.physa.2009.04.023
  contributor:
    fullname: Manzano
– volume: 54
  start-page: 065006
  year: 2021
  ident: ref_95
  article-title: Multidimensional hydrogenic states: Position and momentum expectation values
  publication-title: J. Phys. B At. Mol. Opt. Phys.
  doi: 10.1088/1361-6455/abcdee
  contributor:
    fullname: Dehesa
– volume: 474
  start-page: 233
  year: 2009
  ident: ref_14
  article-title: Renyi complexities and information planes: Atomic structure in conjugated spaces
  publication-title: Chem. Phys. Lett.
  doi: 10.1016/j.cplett.2009.04.061
  contributor:
    fullname: Antolin
– ident: ref_1
– ident: ref_123
– volume: 372
  start-page: 670
  year: 2000
  ident: ref_11
  article-title: Fisher-Shannon plane and statistical complexity of atoms
  publication-title: Phys. Lett. A
  doi: 10.1016/j.physleta.2007.07.077
  contributor:
    fullname: Angulo
– volume: 150
  start-page: 251
  year: 1988
  ident: ref_58
  article-title: A unified theory of polynomial expansions and their applications involving Clebsch-Gordan type linearization relations and Neumann series
  publication-title: Astrophys. Space Sci.
  doi: 10.1007/BF00641720
  contributor:
    fullname: Srivastava
– ident: ref_77
– volume: 380
  start-page: 377
  year: 2016
  ident: ref_7
  article-title: Monotones of statistical complexity measures
  publication-title: Phys. Lett. A
  doi: 10.1016/j.physleta.2015.10.047
  contributor:
    fullname: Rudnicki
– volume: 66
  start-page: 011102
  year: 2002
  ident: ref_15
  article-title: Features of the extension of a statistical measure of complexity to continuous systems
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.66.011102
  contributor:
    fullname: Catalan
– volume: 82
  start-page: 373
  year: 1995
  ident: ref_115
  article-title: Asymptotic behavior of the Lp-norms and the entropy for general orthogonal polynomials
  publication-title: Russ. Acad. Sci. Sbornik Math.
  doi: 10.1070/SM1995v082n02ABEH003571
  contributor:
    fullname: Aptekarev
– ident: ref_109
  doi: 10.1007/978-3-319-99639-4
– volume: 44
  start-page: 129
  year: 1975
  ident: ref_118
  article-title: Uncertainty relations for information entropy in wave mechanics
  publication-title: Comm. Math. Phys.
  doi: 10.1007/BF01608825
  contributor:
    fullname: Mycielski
– volume: 355
  start-page: 87
  year: 2015
  ident: ref_81
  article-title: Role of information theoretic uncertainty relations in quantum theory
  publication-title: Ann. Phys.
  doi: 10.1016/j.aop.2015.01.031
  contributor:
    fullname: Jizba
– volume: 113
  start-page: 48003
  year: 2016
  ident: ref_111
  article-title: Rényi, Shannon and Tsallis entropies of Rydberg hydrogenic systems
  publication-title: EPL
  doi: 10.1209/0295-5075/113/48003
  contributor:
    fullname: Toranzo
– volume: 35
  start-page: 4423
  year: 1994
  ident: ref_114
  article-title: Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials
  publication-title: J. Math. Phys.
  doi: 10.1063/1.530861
  contributor:
    fullname: Aptekarev
– volume: 112
  start-page: 3578
  year: 2012
  ident: ref_52
  article-title: Concurrent phenomena at the transition region of selected elementary chemical reactions: An information-theoretical complexity analysis
  publication-title: Int. J. Quant. Chem.
  doi: 10.1002/qua.24219
  contributor:
    fullname: Esquivel
– volume: 48
  start-page: 043503
  year: 2007
  ident: ref_105
  article-title: Information-theoretic measures of hyperspherical harmonics
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2712913
  contributor:
    fullname: Dehesa
– volume: 312
  start-page: 27
  year: 2003
  ident: ref_10
  article-title: Analysis of signals in the Fisher-Shannon information plane
  publication-title: Phys. Lett. A
  doi: 10.1016/S0375-9601(03)00570-X
  contributor:
    fullname: Vignat
– volume: 121
  start-page: e26424
  year: 2021
  ident: ref_46
  article-title: Cramér-Rao complexity of the confined two-dimensional hydrogen
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.26424
  contributor:
    fullname: Aquino
– volume: 120
  start-page: e26192
  year: 2020
  ident: ref_45
  article-title: Two-dimensional confined hydrogen: An entropy and complexity approach
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.26192
  contributor:
    fullname: Aquino
– ident: ref_59
– ident: ref_62
  doi: 10.3390/sym13081416
– volume: 372
  start-page: 6823
  year: 2008
  ident: ref_19
  article-title: Fisher-Rényi entropy product and information plane
  publication-title: Phys. Lett. A
  doi: 10.1016/j.physleta.2008.10.027
  contributor:
    fullname: Romera
– volume: 47
  start-page: 355
  year: 2000
  ident: ref_5
  article-title: Entanglement monotones
  publication-title: J. Mod. Opt.
  doi: 10.1080/09500340008244048
  contributor:
    fullname: Vidal
– ident: ref_3
– volume: 59
  start-page: 2602
  year: 1999
  ident: ref_75
  article-title: Universal geometric approach to uncertainty, entropy, and information
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.59.2602
  contributor:
    fullname: Hall
– volume: 74
  start-page: 052101
  year: 2006
  ident: ref_82
  article-title: Formulation of the uncertainty relations in terms of the Rényi entropies
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.74.052101
– volume: 41
  start-page: 6600
  year: 2000
  ident: ref_98
  article-title: Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1286984
  contributor:
    fullname: Dehesa
– ident: ref_21
  doi: 10.3390/e19010016
– volume: 50
  start-page: 062107
  year: 2009
  ident: ref_100
  article-title: Inverse momentum expectation values for hydrogenic systems
  publication-title: J. Math. Phys.
  doi: 10.1063/1.3141534
  contributor:
    fullname: Delbourgo
– volume: 54
  start-page: 052109
  year: 2013
  ident: ref_41
  article-title: Entropy and complexity analysis of hydrogenic Rydberg atoms
  publication-title: J. Math. Phys.
  doi: 10.1063/1.4807095
  contributor:
    fullname: Toranzo
– volume: 50
  start-page: 4
  year: 1994
  ident: ref_90
  article-title: Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom
  publication-title: Phys. Rev. A
  contributor:
    fullname: Dehesa
– ident: ref_38
  doi: 10.1103/PhysRevA.106.L021101
– ident: ref_48
  doi: 10.1007/978-90-481-3890-6
– volume: 120
  start-page: e26077
  year: 2020
  ident: ref_103
  article-title: Analytical Shannon information entropies for all discrete multidimensional hydrogenic states
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.26077
  contributor:
    fullname: Toranzo
– volume: 122
  start-page: e26816
  year: 2022
  ident: ref_47
  article-title: An introduction to analysis of Rényi complexity ratio of quantum states for central potential
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.26816
  contributor:
    fullname: Nath
– volume: 128
  start-page: 164109
  year: 2008
  ident: ref_9
  article-title: Atomic complexity measures in position and momentum spaces
  publication-title: J. Chem. Phys.
  doi: 10.1063/1.2907743
  contributor:
    fullname: Angulo
– ident: ref_108
  doi: 10.1007/978-1-4471-6464-7
– volume: 40
  start-page: 5675
  year: 1999
  ident: ref_106
  article-title: Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials
  publication-title: J. Math. Phys.
  doi: 10.1063/1.533051
  contributor:
    fullname: Dehesa
– volume: 47
  start-page: 052104
  year: 2006
  ident: ref_97
  article-title: Fisher information of D-dimensional hydrogenic systems in position and momentum spaces
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2190335
  contributor:
    fullname: Dehesa
– volume: 388
  start-page: 4919
  year: 2009
  ident: ref_50
  article-title: Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields
  publication-title: Phys. A Stat. Mech. Appl.
  doi: 10.1016/j.physa.2009.08.007
  contributor:
    fullname: Dehesa
– volume: 45
  start-page: 1974
  year: 2004
  ident: ref_86
  article-title: A statistical complexity measure with nonextensive entropy and quasi-multiplicativity
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1695600
  contributor:
    fullname: Yamano
– ident: ref_37
  doi: 10.1103/PRXQuantum.3.030340
– volume: 59
  start-page: 123504
  year: 2018
  ident: ref_57
  article-title: Linearization and Krein-like functionals of hypergeometric orthogonal polynomials
  publication-title: J. Math. Phys.
  doi: 10.1063/1.5055299
  contributor:
    fullname: Dehesa
– volume: 20
  start-page: 673
  year: 2001
  ident: ref_33
  article-title: Hyperspherical harmonics as Sturmian orbitals in momentum space: A systematic approach to the few-body Coulomb problem
  publication-title: Int. Rev. Phys. Chem.
  doi: 10.1080/01442350110075926
  contributor:
    fullname: Aquilanti
– volume: 26
  start-page: 488
  year: 2004
  ident: ref_104
  article-title: Computation of the entropy of polynomials orthogonal on an interval
  publication-title: SIAM J. Sci. Comput.
  doi: 10.1137/S1064827503426711
  contributor:
    fullname: Buyarov
– ident: ref_70
– volume: Volume 1
  start-page: 108
  year: 2002
  ident: ref_2
  article-title: Information theoretical approaches to quantum chemistry
  publication-title: Reviews of Modern Quantum Chemistry: A Celebration of the Contributions of Robert G. Parr
  contributor:
    fullname: Sen
– volume: 186
  start-page: 523
  year: 2006
  ident: ref_65
  article-title: Cramér-Rao information plane of orthogonal hypergeometric polynomials
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/j.cam.2005.03.025
  contributor:
    fullname: Dehesa
– volume: 47
  start-page: 103504
  year: 2006
  ident: ref_96
  article-title: Uncertainty relation for Fisher information of D-dimensional single-particle systems with central potentials
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2357998
  contributor:
    fullname: Romera
– volume: 462
  start-page: 1197
  year: 2016
  ident: ref_112
  article-title: Entropic properties of D-dimensional Rydberg systems
  publication-title: Phys. A
  doi: 10.1016/j.physa.2016.06.144
  contributor:
    fullname: Toranzo
– volume: 227
  start-page: 345
  year: 2018
  ident: ref_107
  article-title: Exact Rényi entropies of D-dimensional harmonic systems
  publication-title: Eur. Phys. J.-Sp. Topic
  doi: 10.1140/epjst/e2018-00092-4
  contributor:
    fullname: Toranzo
– volume: 50
  start-page: 123528
  year: 2009
  ident: ref_13
  article-title: A generalized statistical complexity measure: Applications to quantum systems
  publication-title: J. Math. Phys.
  doi: 10.1063/1.3274387
  contributor:
    fullname: Nagy
– volume: 68
  start-page: 212
  year: 2014
  ident: ref_20
  article-title: A generalized complexity measure based on Rényi entropy
  publication-title: Eur. Phys. J. D
  doi: 10.1140/epjd/e2014-50127-2
  contributor:
    fullname: Angulo
– volume: 40
  start-page: 1845
  year: 2007
  ident: ref_102
  article-title: Fisher-information-based uncertainty relation, Cramer-Rao inequality and kinetic energy for the D-dimensional central problem
  publication-title: J. Phys. A: Math. Theor.
  doi: 10.1088/1751-8113/40/8/011
  contributor:
    fullname: Dehesa
– ident: ref_31
  doi: 10.1007/978-94-011-1836-1
– volume: 58
  start-page: 104102
  year: 2017
  ident: ref_74
  article-title: Response to Comment on Entropy and complexity analysis of hydrogenic Rydberg atoms
  publication-title: J. Math. Phys.
  doi: 10.1063/1.4986518
  contributor:
    fullname: Toranzo
– volume: 22
  start-page: 700
  year: 1925
  ident: ref_66
  article-title: Theory of statistical estimation
  publication-title: Proc. Camb. Philos. Soc.
  doi: 10.1017/S0305004100009580
  contributor:
    fullname: Fisher
– volume: 113
  start-page: 140401
  year: 2014
  ident: ref_6
  article-title: Quantifying coherence
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.113.140401
  contributor:
    fullname: Baumgratz
– volume: 45
  start-page: 225303
  year: 2012
  ident: ref_119
  article-title: The Shannon-entropy-based uncertainty relation for D-dimensional central potentials
  publication-title: J. Phys. A Math. Theor.
  doi: 10.1088/1751-8113/45/22/225303
  contributor:
    fullname: Rudnicki
– volume: 39
  start-page: 3050
  year: 1998
  ident: ref_117
  article-title: Strong asymptotics of Laguerre polynomials and information entropies of 2D harmonic oscillator and 1D Coulomb potentials
  publication-title: J. Math. Phys.
  doi: 10.1063/1.532238
  contributor:
    fullname: Dehesa
– volume: 340
  start-page: 131
  year: 2004
  ident: ref_87
  article-title: A statistical measure of complexity with nonextensive entropy
  publication-title: Phys. A
  doi: 10.1016/j.physa.2004.03.087
  contributor:
    fullname: Yamano
– volume: 67
  start-page: 73
  year: 2013
  ident: ref_93
  article-title: D-dimensional Kepler-Coulomb Sturmians and hyperspherical harmonics as complete orthonormal atomic and molecular orbitals
  publication-title: Adv. Quantum Chem.
  doi: 10.1016/B978-0-12-411544-6.00005-4
  contributor:
    fullname: Coletti
– volume: 58
  start-page: 104101
  year: 2017
  ident: ref_73
  article-title: Comment on Entropy and complexity analysis of hydrogenic Rydberg atoms
  publication-title: J. Math. Phys.
  doi: 10.1063/1.5006191
  contributor:
    fullname: Jiao
– volume: 15
  start-page: 4084
  year: 2013
  ident: ref_53
  article-title: Concurrent phenomena at the reaction path of the SN2 Reaction CH3Cl+F-. Information planes and statistical complexity analysis
  publication-title: Entropy
  doi: 10.3390/e15104084
  contributor:
    fullname: Esquivel
– volume: 50
  start-page: 505001
  year: 2017
  ident: ref_24
  article-title: Biparametric complexities and generalized Planck radiation law
  publication-title: J. Phys. A Math. Theor.
  doi: 10.1088/1751-8121/aa95f4
  contributor:
    fullname: Toranzo
– ident: ref_28
  doi: 10.1007/978-90-481-3890-6
– volume: 83
  start-page: 052107
  year: 2011
  ident: ref_84
  article-title: Position-momentum uncertainty relations based on moments of arbitrary order
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.83.052107
  contributor:
    fullname: Zozor
– ident: ref_22
  doi: 10.3390/e19090493
– ident: ref_69
– volume: 54
  start-page: 035305
  year: 2021
  ident: ref_113
  article-title: Rydberg multidimensional states: Rényi and Shannon entropies in momentum space
  publication-title: J. Phys. A Math. Theor.
  doi: 10.1088/1751-8121/abd269
  contributor:
    fullname: Aptekarev
– volume: 122
  start-page: e26858
  year: 2022
  ident: ref_64
  article-title: Algebraic Lq-norms and complexity-like properties of Jacobi polynomials: Degree and parameter asymptotics
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.26858
  contributor:
    fullname: Sobrino
– volume: 387
  start-page: 4800
  year: 2008
  ident: ref_83
  article-title: Some extensions of the uncertainty principle
  publication-title: Phys. A
  doi: 10.1016/j.physa.2008.04.010
  contributor:
    fullname: Zozor
– volume: 125
  start-page: 07411
  year: 2006
  ident: ref_101
  article-title: Information entropies for eigendensities of homogeneous potentials
  publication-title: J. Chem. Phys.
  doi: 10.1063/1.2263710
  contributor:
    fullname: Sen
– volume: 44
  start-page: 065301
  year: 2011
  ident: ref_85
  article-title: A quantum uncertainty relation based on Fisher’s information
  publication-title: J. Phys. A Math. Theor.
  doi: 10.1088/1751-8113/44/6/065301
  contributor:
    fullname: Plastino
– volume: 390
  start-page: 2215
  year: 2011
  ident: ref_49
  article-title: Entropy and complexity analysis of Dirac-delta-like quantum potentials
  publication-title: Phys. A Stat. Mech. its Appl.
  doi: 10.1016/j.physa.2011.02.020
  contributor:
    fullname: Bouvrie
– volume: 84
  start-page: 042105
  year: 2011
  ident: ref_89
  article-title: Upper bounds on quantum uncertainty products and complexity measures
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.84.042105
  contributor:
    fullname: Guerrero
– volume: 32
  start-page: 7345
  year: 1999
  ident: ref_54
  article-title: General linearization formulas for products of continuous hypergeometric-type polynomials
  publication-title: J. Phys. A
  doi: 10.1088/0305-4470/32/42/308
  contributor:
    fullname: Dehesa
– volume: 223
  start-page: 348
  year: 1996
  ident: ref_40
  article-title: Some features of the López-Ruiz-Mancini-Calbet (LMC) statistical measure of complexity
  publication-title: Phys. Lett. A
  doi: 10.1016/S0375-9601(96)00756-6
  contributor:
    fullname: Anteneodo
– ident: ref_72
– volume: 110
  start-page: 1529
  year: 2010
  ident: ref_4
  article-title: Information theory of D-dimensional hydrogenic systems: Application to circular and Rydberg states
  publication-title: Int. J. Quantum Chem.
  doi: 10.1002/qua.22244
  contributor:
    fullname: Dehesa
– volume: 233
  start-page: 1355
  year: 2010
  ident: ref_61
  article-title: Asymptotics of orthogonal polynomials’ entropy
  publication-title: J. Comp. Appl. Math.
  doi: 10.1016/j.cam.2009.02.056
  contributor:
    fullname: Aptekarev
– ident: ref_121
  doi: 10.3390/e24111590
– volume: 687
  start-page: 322
  year: 2017
  ident: ref_42
  article-title: Various complexity measures in confined hydrogen atom
  publication-title: Chem. Phys. Lett.
  doi: 10.1016/j.cplett.2017.09.036
  contributor:
    fullname: Majumdar
– volume: 133
  start-page: 23
  year: 2001
  ident: ref_60
  article-title: Quantum information entropies and orthogonal polynomials
  publication-title: J. Comput. Appl. Math.
  doi: 10.1016/S0377-0427(00)00633-6
  contributor:
    fullname: Dehesa
– volume: 36
  start-page: 2153
  year: 2008
  ident: ref_78
  article-title: A class of Rényi information estimators for multidimensional densities
  publication-title: Ann. Stat.
  doi: 10.1214/07-AOS539
  contributor:
    fullname: Leonenko
– volume: 40
  start-page: 625
  year: 1999
  ident: ref_35
  article-title: Is there a stable hydrogen atom in higher dimensions?
  publication-title: J. Math. Phys.
  doi: 10.1063/1.532679
  contributor:
    fullname: Burgbacher
– volume: 223
  start-page: 25
  year: 2013
  ident: ref_55
  article-title: Rényi entropies, Lq norms and linearization of powers of hypergeometric orthogonal polynomials by means of multivariate special function
  publication-title: Appl. Math. Comput.
  doi: 10.1016/j.amc.2013.07.076
  contributor:
    fullname: Dehesa
– ident: ref_92
  doi: 10.1142/6107
– volume: 55
  start-page: 539
  year: 2009
  ident: ref_110
  article-title: Configuration complexities of hydrogenic atoms
  publication-title: Eur. Phys. J. D
  doi: 10.1140/epjd/e2009-00251-1
  contributor:
    fullname: Dehesa
– volume: 58
  start-page: 103302
  year: 2017
  ident: ref_122
  article-title: Entropic uncertainty measures for large dimensional hydrogenic systems
  publication-title: J. Math. Phys.
  doi: 10.1063/1.5006569
  contributor:
    fullname: Temme
– volume: 109
  start-page: 586
  year: 2009
  ident: ref_8
  article-title: Complexity analysis of ionization processes and isoelectronic series
  publication-title: Int. J. Quant. Chem.
  doi: 10.1002/qua.21832
  contributor:
    fullname: Angulo
– ident: ref_36
  doi: 10.1088/2058-9565/aca996
– volume: 101
  start-page: 042511
  year: 2020
  ident: ref_99
  article-title: Coulomb expectation values in D = 3 and D = 3 − 2e dimensions
  publication-title: Phys. Rev. A
  doi: 10.1103/PhysRevA.101.042511
  contributor:
    fullname: Adkins
– ident: ref_67
  doi: 10.1017/CBO9780511616907
– volume: 388
  start-page: 2081
  year: 2009
  ident: ref_27
  article-title: Rigorous properties and uncertainty-like relationships on product-complexity measures: Applications to atomic systems
  publication-title: Phys. A
  doi: 10.1016/j.physa.2009.01.037
  contributor:
    fullname: Angulo
– volume: 57
  start-page: 1806
  year: 2019
  ident: ref_43
  article-title: Quantum mechanical virial-like theorem for confined quantum systems
  publication-title: J. Math. Chem.
  doi: 10.1007/s10910-019-01039-8
  contributor:
    fullname: Mukherjee
– volume: 2018
  start-page: 073203
  year: 2018
  ident: ref_56
  article-title: Rényi entropies for multidimensional hydrogenic systems in position and momentum spaces
  publication-title: J. Stat. Mech.
  doi: 10.1088/1742-5468/aacf0c
  contributor:
    fullname: Toranzo
– volume: 2017
  start-page: 043408
  year: 2017
  ident: ref_23
  article-title: The biparametric Fisher-Rényi complexity measure and its application to the multidimensional blackbody radiation
  publication-title: J. Stat. Mech. Theory Exp.
  doi: 10.1088/1742-5468/aa6a22
  contributor:
    fullname: Toranzo
– volume: 115
  start-page: 215
  year: 2005
  ident: ref_16
  article-title: Shannon information, LMC complexity and Rényi entropies: A straightforward approach
  publication-title: Biophys. Chem.
  doi: 10.1016/j.bpc.2004.12.035
– volume: 99
  start-page: 153
  year: 1999
  ident: ref_120
  article-title: Martinez-Finklshtein and E. B. Saff, Asymptotics of the information entropy for Jacobi and Laguerre polynomials with varying weights
  publication-title: J. Approx. Theory
  doi: 10.1006/jath.1998.3315
  contributor:
    fullname: Buyarov
– ident: ref_26
  doi: 10.1007/978-90-481-3890-6
– volume: 120
  start-page: 8906
  year: 2004
  ident: ref_12
  article-title: The Fisher–Shannon information plane, an electron correlation tool
  publication-title: J. Chem. Phys.
  doi: 10.1063/1.1697374
  contributor:
    fullname: Romera
– volume: 366
  start-page: 120
  year: 2007
  ident: ref_34
  article-title: Electronic states of a hydrogenic donor impurity in semiconductor nano-structures
  publication-title: Phys. Lett. A
  doi: 10.1016/j.physleta.2007.02.028
  contributor:
    fullname: Li
– volume: 25
  start-page: 1689
  year: 2012
  ident: ref_76
  article-title: Generalized Cramér-Rao relations for non-relativistic quantum systems
  publication-title: Appl. Math. Lett.
  doi: 10.1016/j.aml.2012.01.038
  contributor:
    fullname: Dehesa
– volume: 3
  start-page: 207
  year: 2009
  ident: ref_18
  article-title: Generalized Statistical Complexity and Fisher–Rényi Entropy Product in the H-Atom
  publication-title: Int. Rev. Phys.
  contributor:
    fullname: Romera
– volume: 37
  start-page: 1501
  year: 1991
  ident: ref_88
  article-title: Information theoretic inequalities
  publication-title: IEEE Trans. Inform. Theor.
  doi: 10.1109/18.104312
  contributor:
    fullname: Dembo
– volume: 26
  start-page: 150
  year: 2012
  ident: ref_30
  article-title: Complexity of multidimensional hydrogenic systems
  publication-title: Ind. J. Appl. Math. Stat.
  contributor:
    fullname: Dehesa
– volume: 59
  start-page: 1459
  year: 1999
  ident: ref_25
  article-title: Simple measure for complexity
  publication-title: Phys. Rev. E
  doi: 10.1103/PhysRevE.59.1459
  contributor:
    fullname: Shiner
– volume: 209
  start-page: 321
  year: 1995
  ident: ref_39
  article-title: A statistical measure of complexity
  publication-title: Phys. Lett. A
  doi: 10.1016/0375-9601(95)00867-5
  contributor:
    fullname: Mancini
– ident: ref_91
– volume: Volume 1
  start-page: 547
  year: 1961
  ident: ref_71
  article-title: On measures of information and entropy
  publication-title: Proceedings Fourth Berkeley Symposium on Mathematical Statistics and Probability
  contributor:
    fullname: Neyman
– volume: 2017
  start-page: 083102
  year: 2017
  ident: ref_17
  article-title: Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
  publication-title: J. Stat. Mech. Theory Exp.
  doi: 10.1088/1742-5468/aa7df4
  contributor:
    fullname: Toranzo
– volume: 53
  start-page: 47
  year: 1996
  ident: ref_116
  article-title: Asymptotics of entropy integrals for orthogonal polynomials
  publication-title: Dokl. Math.
  contributor:
    fullname: Aptekarev
– volume: 414
  start-page: 468
  year: 2005
  ident: ref_68
  article-title: The Fisher information of single-particle systems with a central potential
  publication-title: Chem. Phys. Lett.
  doi: 10.1016/j.cplett.2005.08.032
  contributor:
    fullname: Romera
– ident: ref_32
  doi: 10.1002/0470010827
SSID ssj0002802968
Score 2.2709901
Snippet Statistical measures of complexity hold significant potential for applications in D-dimensional finite fermion systems, spanning from the quantification of the...
SourceID doaj
proquest
crossref
SourceType Open Website
Aggregation Database
StartPage 116
SubjectTerms Charged particles
Chemical reactions
Complexity
Cramér–Rao complexity-like measures
Entropy
Fermions
First principles
Fisher–Shannon complexity-like measures
Fourier transforms
highly excited Rydberg states
Hypergeometric functions
LMC–Rényi complexity-like measures
Mathematical analysis
multidimensional hydrogenic systems
Polynomials
Rydberg states
SummonAdditionalLinks – databaseName: AUTh Library subscriptions: ProQuest Central
  dbid: BENPR
  link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3NTtwwELYKXHpBoLbq8icfKvVSC8exk_iEYAVaVV1UbUHiFvkvZQW7gexy2BvvwFPwHLwJT9KZxAtCSD1FiXNIPPb4-2bsbwj5ZsEbmoIbJmxumdTOsCLlFSuCUjZUmXdtjaXhaTY4lz8v1EUMuM3itsqlT2wdta8dxsj3RQ5ABkVU04ObW4ZVozC7GktorJA1kUhM064dHZ_-Hr1EWUTBhc6KTq0xBX4P_BC--G6iOAa29ZvVqBXtf-eT24XmZIOsR4RIDzuTbpIPYfqJPPQbM3l6bJ7vH0am_kG7iuVw9-fSTIHBUzP19Newj-1Pj9PFmOJER7HL-YJdj68CHXbBwBmtK9qeuvWo699pctDBwjc1DKWxo1HCnGKAlh6-prfpvKajhcftYLRDqJ_J-cnxWX_AYj0F5lLoPqZDkHllcyUc1q9LDIAPnnkAQZ4bAcDMVlo7roXlTvFgKoN5mYBWE5VVIf1CVuGPwldCpROYX81Qrgsu2gDTEl4bqbyUqlI98n3Zr-VNJ5tRAt1AC5RvLdAjR9jtL2-h3HX7oG7-lnH2lIlXzulE5D54aZUyQIMsENdEA-Dhhe-RnaXRyjgHZ-XriNn6f_M2-YhF5Lu92Dtkdd7chV2AGnO7F8fTP_Sh2ws
  priority: 102
  providerName: ProQuest
Title Cramér–Rao, Fisher–Shannon and LMC–Rényi Complexity-like Measures of Multidimensional Hydrogenic Systems with Application to Rydberg States
URI https://www.proquest.com/docview/2791699223
https://doaj.org/article/1d5cc9127ded4b55a597b1071975008d
Volume 5
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1JTsMwFLUYNmwQCBCFUnmBxIYIx4mTeAkVpUIUoUKl7iJPEWVoUVsW3XEHTsE5uAkn4f84TGLBhlWUQUrs5-G9b-d9QnY1jIYqYyrgOtVBLI0KsogVQeaE0K5IrClzLHXOk3YvPu2L_rdUX7gnzNsD-4o7CK0wRoY8tc7GWggFDFiDZgklzHUss-XoG4pvYuqmDBkxLpPMuzRGoOtBF8KXPt4LhgFt-WMWKs36f43F5QTTWiHLFTOkh_6LVsmcG66R5-ZY3b--jN-enrtqtE99pnI4u7xWQ1DuVA0tPes08f7ry3A2oNjB0eRyOgvuBreOdnwQcEJHBS3_trXo5--9OGh7ZscjaEIDQyvrcoqBWXr4taxNpyPanVncBkY9M10nvdbxVbMdVHkUAhPxVAbSuTgtdCq4wbx1oQLSwRIL5McyxYGQ6UJKwyTXzAjmVKFwPcYhWrzQwkUbZAFK5DYJjQ3HddUEbbrgIBUoLG6lioWNY1GIGtn7qNf8wdtl5CAzEIH8JwI1coTV_vkU2lyXFwD8vAI__wv8Gql_gJZXfW-SQ5HDBO12o63_eMc2WcIU836ndp0sTMePbgeIyFQ3yHzWOmmQxaPj84tuo2yB76Zv4_E
link.rule.ids 315,786,790,870,2115,12792,21416,27955,27956,33406,33777,43633,43838,74390,74657
linkProvider Directory of Open Access Journals
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3NTuMwELb4OexeECtA24Xd9QGJCxauYyfxCUFFKdBy4EfiFvkvULE0kJZDb_sOPAXPwZvskzCTpCC0EqcocQ6JZzz5vhnnG0I2LURDk3LDhE0sk9oZlkY8Z2lQyoY89q7qsTQ4jXuX8vhKXTUJt3GzrXIWE6tA7QuHOfIdkQCQQRHVaPf-gWHXKKyuNi005smijOII_TztHr7lWETKhY7TWqsxAnYP7BCe9_FOcUxr6w_fokqy_7-IXH1mustkqcGHdK826DcyF0Yr5KlTmruX5_Lf36czU2zTul85nJ3fmBHwd2pGnvYHHRx_eR5NhxSXOUpdTqbsz_A20EGdChzTIqfVP7ceVf1rRQ7am_qyAEcaOtoImFNMz9K99-I2nRT0bOpxMxit8ekqueweXHR6rOmmwFwEk8d0CDLJbaKEw-51bQPQg8ceIJDnRgAss7nWjmthuVM8mNxgVSagzURuVYjWyAK8UfhOqHQCq6sxinXBQRvgWcJrI5WXUuWqRbZm85rd16IZGZANtED20QItso_T_nYXil1XF4ryOmvWTtb2yjndFokPXlqlDJAgC7S1rQHu8NS3yMbMaFmzAsfZu7_8-Hz4N_nSuxj0s_7R6ck6-Yrt5Otd2RtkYVI-hp8AOib2V-VZr7aL3JI
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3LTtwwFLUKlSo2qFVbMUCLF5W6qYXHiZN4hWDKdNoyqKIgsYv8hBEwgcywmB3_wFfwHfxJv6T3Jh4QQmIVJc4i8b12zn3kHEK-GNgNdcE1EyY3LFVWsyLhgRVeSuND5myjsTTczwZH6a9jeRz7nyaxrXK-JzYbtass5sg3RQ5ABklUk80Q2yL-fO9vXV4xVJDCSmuU01ggrxFko4xD0f_xkG8RBRcqK1rexgTGIVKEZ7--kBxT3OrJd6mh73-2OzefnP5bshyxIt1ujfuOvPLj9-S2V-uL-7v6383tga6-0Va7HM7-nuoxxPJUjx3dG_Zw_P5uPBtRXPJIezmdsfPRmafDNi04oVWgzf-3Dhn-W3YOOpi5ugKnGlkaycwppmrp9mOhm04rejBz2BhGW6z6gRz1dw97AxaVFZhNYCKZ8j7Ng8mlsKhk19UAQ3jmAA45rgVANBOUslwJw63kXgeNFRqP9hPBSJ98JIvwRn6F0NQKrLRmSNwFB6Uh5hJO6VS6NJVBdsjX-byWly2BRgmBB1qgfGqBDtnBaX-4C4mvmwtVfVLGdVR2nbRWdUXuvEuNlBoCIgMhbFcB9OGF65D1udHKuBon5aPvrL48vEHegFOVez_3f6-RJVSWbxu018nitL72nwB_TM3nxrH-A5E64Mc
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Cram%C3%A9r%E2%80%93Rao%2C+Fisher%E2%80%93Shannon+and+LMC%E2%80%93R%C3%A9nyi+Complexity-like+Measures+of+Multidimensional+Hydrogenic+Systems+with+Application+to+Rydberg+States&rft.jtitle=Quantum+reports&rft.au=Jes%C3%BAs+S.+Dehesa&rft.date=2023-02-01&rft.pub=MDPI+AG&rft.eissn=2624-960X&rft.volume=5&rft.issue=1&rft.spage=116&rft.epage=137&rft_id=info:doi/10.3390%2Fquantum5010009&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_1d5cc9127ded4b55a597b1071975008d
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2624-960X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2624-960X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2624-960X&client=summon