Discrete quantum mechanics

A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solutio...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 44; no. 35; pp. 353001 - 47
Main Authors Odake, Satoru, Sasaki, Ryu
Format Journal Article
LanguageEnglish
Published Bristol IOP 02.09.2011
Subjects
Algebra
Exact sciences and technology
Mathematical analysis
Physics
Pictures
Polynomials
Quantum mechanics
Schroedinger equation
Solution space
Symmetry
Hamiltonians
Quantum mechanics
Dynamical symmetry
Unified theory
Annihilation operators
Schroedinger equation
Creation operators
Invariance
Heisenberg picture
Solvability
Orthogonal polynomial
Online AccessGet full text

Cover

Abstract A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrodinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrodinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two newinfinite families of orthogonal polynomials, the X sub(l)Meixner-Pollaczek and the X sub(l)Meixner polynomials, are reported.
AbstractList A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorized Hamiltonians, the general structure of the solution spaces of the Schrodinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schrodinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, the unified theory of exact and quasi-exact solvability based on the sinusoidal coordinates, and the infinite families of new orthogonal (the exceptional) polynomials. Two newinfinite families of orthogonal polynomials, the X sub(l)Meixner-Pollaczek and the X sub(l)Meixner polynomials, are reported.
Author Sasaki, Ryu
Odake, Satoru
Author_xml – sequence: 1
  givenname: Satoru
  surname: Odake
  fullname: Odake, Satoru
– sequence: 2
  givenname: Ryu
  surname: Sasaki
  fullname: Sasaki, Ryu
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24522654$$DView record in Pascal Francis
BookMark eNqFkE1LAzEQhoNUsK3-AQ_Si-BlbSYfuy14kdYvKHjRc5hOsxjZzbZJ9uC_N6XVgxdhYAbmfecdnhEb-M5bxq6A3wKfzaZQaShmAHKq1FTqXJJzOGHD40LA4HcGecZGMX5yrhWfiyG7XLpIwSY72fXoU99OWksf6B3Fc3ZaYxPtxbGP2fvjw9viuVi9Pr0s7lcFyVKkQtZqI3mFiGW13miLim8EV1og1RzmsrRKU245fE5Kg1rrEqiqxFqjJkI5ZjeHu9vQ7Xobk2nzT7Zp0NuujwZKwbkCpWWWXh-lGAmbOqAnF802uBbDlxE5VZRaZd3dQUehizHY2pBLmFznU0DXGOBmj87sqZg9FaOUkdoc0GV7-cf-k_CP8Rs8FnEh
CitedBy_id crossref_primary_10_1063_1_4941087
crossref_primary_10_1063_1_5021462
crossref_primary_10_1063_1_4921230
crossref_primary_10_1103_PhysRevB_106_094205
crossref_primary_10_1063_1_4966985
crossref_primary_10_1063_1_4880200
crossref_primary_10_1016_j_physleta_2016_08_047
crossref_primary_10_1002_andp_202300488
crossref_primary_10_1063_1_4918707
crossref_primary_10_1093_ptep_pty076
crossref_primary_10_1063_1_4744964
crossref_primary_10_1093_ptep_ptad077
crossref_primary_10_1093_ptep_ptx165
crossref_primary_10_1063_5_0207300
crossref_primary_10_1093_ptep_ptz124
crossref_primary_10_1016_j_heliyon_2024_e34402
crossref_primary_10_1103_PhysRevA_96_042106
crossref_primary_10_1142_S021797921350135X
crossref_primary_10_1007_s12043_019_1787_2
crossref_primary_10_1063_1_5038057
crossref_primary_10_1016_j_aop_2014_06_016
crossref_primary_10_1016_j_jmaa_2024_128591
crossref_primary_10_1016_j_jmaa_2012_10_032
crossref_primary_10_1063_5_0006440
crossref_primary_10_1063_5_0152234
crossref_primary_10_1007_s00220_015_2467_9
crossref_primary_10_1007_s00220_019_03323_9
crossref_primary_10_1038_s41467_024_49747_3
crossref_primary_10_1063_1_5144338
crossref_primary_10_1093_ptep_ptx051
crossref_primary_10_1063_1_4826475
crossref_primary_10_1016_j_jat_2014_04_009
crossref_primary_10_1063_1_3671966
crossref_primary_10_1007_s11785_016_0544_5
crossref_primary_10_1016_j_aop_2014_09_022
crossref_primary_10_1063_1_4819255
crossref_primary_10_1063_1_4926351
crossref_primary_10_1063_1_4859795
Cites_doi 10.1007/BF01017247
10.1063/1.1927080
10.1016/0370-1573(94)00080-M
10.1007/BF02748213
10.1016/j.physletb.2009.12.062
10.1017/CBO9781107325937
10.1016/j.physletb.2008.03.043
10.1103/PhysRevD.20.1342
10.1137/0513044
10.2991/jnmp.2005.12.s1.53
10.1143/PTP.126.1
10.1088/0305-4470/28/10/002
10.1063/1.1367328
10.1088/0305-4470/32/1/013
10.1143/PTP.114.1245
10.1063/1.3215983
10.1016/j.physletb.2006.08.017
10.1007/s11232-008-0044-5
10.1088/0305-4470/35/33/306
10.1088/1751-8113/42/40/404009
10.1006/aphy.1998.5856
10.1063/1.1429321
10.1088/1751-8113/43/33/335201
10.1088/0305-4470/28/13/003
10.1088/1751-8113/43/31/315204
10.1063/1.1665604
10.1063/1.2898695
10.1088/0305-4470/37/49/006
10.1007/978-3-642-61544-3
10.1016/0003-4916(92)90336-K
10.1063/1.2818560
10.1098/rsta.2010.0262
10.1155/S1073792897000251
10.1143/PTP.122.1067
10.1016/j.cam.2006.11.004
10.1007/BF01035458
10.1143/PTP.124.1
10.1007/BF01466727
10.1103/PhysRevD.20.1332
10.1016/S0375-9601(97)00422-2
10.1006/aphy.2001.6169
10.4310/MAA.1999.v6.n3.a1
10.1007/BF01207363
10.1016/j.jat.2009.11.002
10.1007/BF01180560
10.1016/0375-9601(93)90137-O
10.1088/0305-4470/34/44/313
10.1093/qmath/6.1.121
10.1016/S0377-0427(99)00090-4
10.1016/0022-247X(69)90037-7
10.1016/S0370-2693(01)00250-7
10.1007/s12043-009-0126-4
10.1007/BF01614245
10.2991/jnmp.2005.12.s1.41
10.1016/0377-0427(95)00262-6
10.1063/1.531122
10.1007/BF00760860
10.1063/1.530498
10.1007/978-1-4899-1219-0_5
10.2991/jnmp.2008.15.s3.36
10.1007/BF02785163
10.1143/PTP.119.663
10.1007/BF01015906
10.1088/0305-4470/37/2/015
10.1103/PhysRevLett.41.207
10.1016/0001-8708(75)90151-6
10.1088/0305-4470/34/28/303
10.1016/S0550-3213(01)00389-3
10.1007/978-3-642-74748-9
10.1103/RevModPhys.23.21
10.1016/0550-3213(81)90006-7
10.1143/PTP.125.851
10.1103/PhysRevA.5.1372
10.1088/1751-8113/40/31/009
10.1016/0003-4916(86)90097-7
10.1142/S0217751X90000374
10.1090/coll/023
10.1063/1.3339676
10.1143/PTP.103.463
10.1088/0305-4470/34/47/502
10.1063/1.2349485
10.1016/j.physletb.2009.10.078
10.1112/plms/s1-16.1.245
10.1016/0375-9601(93)91182-5
10.1016/j.jmaa.2009.05.052
10.1016/j.physletb.2009.08.004
10.1017/CBO9780511526251
10.1016/S0375-9601(01)00249-3
10.1088/0305-4470/33/49/303
10.1017/CBO9781107325982
10.1088/0305-4470/37/35/008
10.1103/PhysRevD.20.1321
10.1088/0305-4470/30/21/030
10.1088/0305-4470/21/4/002
ContentType Journal Article
Copyright 2015 INIST-CNRS
Copyright_xml – notice: 2015 INIST-CNRS
DBID AAYXX
CITATION
IQODW
7U5
8FD
H8D
L7M
DOI 10.1088/1751-8113/44/35/353001
DatabaseName CrossRef
Pascal-Francis
Solid State and Superconductivity Abstracts
Technology Research Database
Aerospace Database
Advanced Technologies Database with Aerospace
DatabaseTitle CrossRef
Aerospace Database
Solid State and Superconductivity Abstracts
Technology Research Database
Advanced Technologies Database with Aerospace
DatabaseTitleList Aerospace Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 1751-8121
EndPage 47
ExternalDocumentID 24522654
10_1088_1751_8113_44_35_353001
GroupedDBID 1JI
1WK
4.4
5B3
5GY
5VS
5ZH
5ZI
6TJ
7.M
7.Q
AAGCD
AAGID
AAJIO
AAJKP
AALHV
AATNI
AAYXX
ABCXL
ABHWH
ABQJV
ABVAM
ACAFW
ACGFS
ACHIP
ACNCT
ADEQX
AEFHF
AERVB
AFYNE
AKPSB
ALMA_UNASSIGNED_HOLDINGS
AOAED
ASPBG
ATQHT
AVWKF
AZFZN
BBWZM
CITATION
CJUJL
CRLBU
CS3
EBS
EDWGO
EJD
EMSAF
EPQRW
EQZZN
FEDTE
HVGLF
IHE
IJHAN
IOP
IZVLO
JCGBZ
KOT
LAP
M45
N5L
NT-
NT.
PJBAE
Q02
RIN
RNS
RO9
ROL
RPA
SY9
TN5
W28
02O
AFFNX
CBCFC
CEBXE
H~9
IQODW
7U5
8FD
H8D
L7M
ID FETCH-LOGICAL-c362t-3f4d307aaa67bd5ea40d20452acf01936e45c9368119c4514b561c772b5a5cca3
ISSN 1751-8113
IngestDate Fri Jul 11 16:06:40 EDT 2025
Mon Jul 21 09:15:35 EDT 2025
Tue Jul 01 02:32:25 EDT 2025
Thu Apr 24 22:52:55 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 35
Keywords Hamiltonians
Quantum mechanics
Dynamical symmetry
Unified theory
Annihilation operators
Schroedinger equation
Creation operators
Invariance
Heisenberg picture
Solvability
Orthogonal polynomial
Language English
License CC BY 4.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c362t-3f4d307aaa67bd5ea40d20452acf01936e45c9368119c4514b561c772b5a5cca3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
OpenAccessLink https://soar-ir.repo.nii.ac.jp/records/11740
PQID 1620041453
PQPubID 23500
PageCount 47
ParticipantIDs proquest_miscellaneous_1620041453
pascalfrancis_primary_24522654
crossref_citationtrail_10_1088_1751_8113_44_35_353001
crossref_primary_10_1088_1751_8113_44_35_353001
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2011-09-02
PublicationDateYYYYMMDD 2011-09-02
PublicationDate_xml – month: 09
  year: 2011
  text: 2011-09-02
  day: 02
PublicationDecade 2010
PublicationPlace Bristol
PublicationPlace_xml – name: Bristol
PublicationTitle Journal of physics. A, Mathematical and theoretical
PublicationYear 2011
Publisher IOP
Publisher_xml – name: IOP
References 88
89
Odake S (119) 2005; 18
Gazeau J P (77) 1999; 32
112
113
Darboux G (59) 1882; 94
114
90
Gómez-Ullate D (107) 2010; 43
Ismail M E H (5) 2005
91
118
93
94
95
96
97
10
11
Corrigan E (108) 2002; 35
12
15
19
Koekoek R Swarttouw R F (6) 1996
Odake S (20) 2008; 49
Gómez-Ullate D Kamran N Milson R (101) 2011
120
1
4
7
8
Floreanini R (84) 1995; 28
Terwilliger P (34) 2004
21
22
24
25
26
27
Stieltjes T (109) 1885; 100
29
Gendenshtein L E (30) 1983; 38
Odake S (14) 2006; 47
32
Odake S (16) 2007; 48
35
Chihara T S (70) 1978
van Diejen J F (57) 1996
Gaillard P (60) 2009; 42
Spiridonov V (43) 1997; 30
Andrews G E (3) 1999
Risken H (67) 1996
Odake S (39) 2011; 44
40
41
42
44
46
47
48
49
Dabrowska J W (31) 1988; 21
Vinet L (75) 2008; 4
Askey R (83) 1993; 6
Odake S (13) 2005; 46
50
52
53
Ho C-L Odake S Sasaki R (9) 2009
54
56
Parthasarathy P R (68) 2004
58
Odake S (117) 2005; 46
Sasaki R (69) 2009; 50
Szegö G (111) 1939
Sasaki R (99) 2001; 34
Ushveridze A G (98) 1988; 2
Quesne C (105) 2009; 5
van Diejen J F (55) 1995; 28
Bannai E (33) 1984
Odake S (38) 2010; 43
Stieltjes T (110) 1885; 100
61
62
63
64
Quesne C (92) 2008; 41
65
Odake S (17) 2007; 48
Khastgir S P (51) 2000; 33
Sasaki R (100) 2001; 34
Krein M G (28) 1957; 113
Dutta D (106) 2010; 51
Odake S (23) 2010; 51
Sasaki R (18) 2007; 48
71
72
73
Ragnisco O (115) 2004; 37
74
76
78
79
Odake S (36) 2010; 51
Alexio A N F (81) 2004; 37
Ho C-L Sasaki R (102) 2011
Nikiforov A F (2) 1991
Atakishiyev M N (85) 2007; 40
Yermolayeva O (66) 1999; 6
103
104
Odake S (116) 2004; 37
Sasaki R (37) 2010; 43
80
82
Bangerezako G (45) 2001; 34
86
87
References_xml – ident: 82
  doi: 10.1007/BF01017247
– volume: 46
  year: 2005
  ident: 117
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1927080
– ident: 62
  doi: 10.1016/0370-1573(94)00080-M
– ident: 112
  doi: 10.1007/BF02748213
– ident: 8
  doi: 10.1016/j.physletb.2009.12.062
– year: 1999
  ident: 3
  publication-title: Special Functions
  doi: 10.1017/CBO9781107325937
– ident: 19
  doi: 10.1016/j.physletb.2008.03.043
– ident: 74
  doi: 10.1103/PhysRevD.20.1342
– ident: 32
  doi: 10.1137/0513044
– ident: 120
  doi: 10.2991/jnmp.2005.12.s1.53
– ident: 26
  doi: 10.1143/PTP.126.1
– volume: 28
  start-page: L287
  issn: 0305-4470
  year: 1995
  ident: 84
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/28/10/002
– volume: 100
  start-page: 620
  year: 1885
  ident: 110
  publication-title: Comptes Rendus
– volume: 44
  issn: 1751-8113
  year: 2011
  ident: 39
  publication-title: J. Phys. A: Math. Theor.
– year: 1996
  ident: 6
– ident: 78
  doi: 10.1063/1.1367328
– volume: 41
  issn: 1751-8113
  year: 2008
  ident: 92
  publication-title: J. Phys. A: Math. Theor.
– volume: 32
  start-page: 123
  issn: 0305-4470
  year: 1999
  ident: 77
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/32/1/013
– ident: 118
  doi: 10.1143/PTP.114.1245
– year: 2004
  ident: 34
  publication-title: Universidad Carlos III de Madrid, Leganes, Spain
– volume: 50
  year: 2009
  ident: 69
  publication-title: J. Math. Phys.
  doi: 10.1063/1.3215983
– ident: 15
  doi: 10.1016/j.physletb.2006.08.017
– ident: 86
  doi: 10.1007/s11232-008-0044-5
– volume: 35
  start-page: 7017
  issn: 0305-4470
  year: 2002
  ident: 108
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/35/33/306
– volume: 43
  issn: 1751-8113
  year: 2010
  ident: 107
  publication-title: J. Phys. A: Math. Theor.
– volume: 42
  issn: 1751-8113
  year: 2009
  ident: 60
  publication-title: J. Phys. A: Math. Theor.
  doi: 10.1088/1751-8113/42/40/404009
– ident: 104
  doi: 10.1006/aphy.1998.5856
– ident: 80
  doi: 10.1063/1.1429321
– volume: 43
  issn: 1751-8113
  year: 2010
  ident: 38
  publication-title: J. Phys. A: Math. Theor.
  doi: 10.1088/1751-8113/43/33/335201
– volume: 28
  start-page: L369
  issn: 0305-4470
  year: 1995
  ident: 55
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/28/13/003
– volume: 5
  start-page: 084
  year: 2009
  ident: 105
  publication-title: SIGMA
– volume: 43
  issn: 1751-8113
  year: 2010
  ident: 37
  publication-title: J. Phys. A: Math. Theor.
  doi: 10.1088/1751-8113/43/31/315204
– volume: 2
  start-page: 50, 54–8
  year: 1988
  ident: 98
  publication-title: Sov. Phys.—Lebedev Inst. Rep.
– volume: 51
  year: 2010
  ident: 23
  publication-title: J. Math. Phys.
– year: 2009
  ident: 9
– year: 2004
  ident: 68
  publication-title: Birth and Death Processes (BDP) Models with Applications
– ident: 47
  doi: 10.1063/1.1665604
– volume: 49
  year: 2008
  ident: 20
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2898695
– volume: 37
  start-page: 11841
  issn: 0305-4470
  year: 2004
  ident: 116
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/37/49/006
– year: 1996
  ident: 67
  publication-title: The Fokker–Planck Equation
  doi: 10.1007/978-3-642-61544-3
– ident: 87
  doi: 10.1016/0003-4916(92)90336-K
– year: 2011
  ident: 101
– volume: 48
  year: 2007
  ident: 18
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2818560
– ident: 40
  doi: 10.1098/rsta.2010.0262
– volume: 4
  start-page: 015
  year: 2008
  ident: 75
  publication-title: SIGMA
– volume: 18
  start-page: 85
  year: 2005
  ident: 119
  publication-title: Rokko Lectures Math. (Kobe University)
– ident: 1
  doi: 10.1155/S1073792897000251
– ident: 24
  doi: 10.1143/PTP.122.1067
– ident: 95
  doi: 10.1016/j.cam.2006.11.004
– ident: 29
  doi: 10.1007/BF01035458
– volume: 38
  start-page: 356
  year: 1983
  ident: 30
  publication-title: JETP Lett.
– ident: 25
  doi: 10.1143/PTP.124.1
– ident: 97
  doi: 10.1007/BF01466727
– ident: 73
  doi: 10.1103/PhysRevD.20.1332
– ident: 103
  doi: 10.1016/S0375-9601(97)00422-2
– volume: 46
  year: 2005
  ident: 13
  publication-title: J. Math. Phys.
  doi: 10.1063/1.1927080
– ident: 58
  doi: 10.1006/aphy.2001.6169
– volume: 6
  start-page: 1
  issn: 1073-2772
  year: 1999
  ident: 66
  publication-title: Methods Appl. Anal.
  doi: 10.4310/MAA.1999.v6.n3.a1
– volume: 100
  start-page: 439
  year: 1885
  ident: 109
  publication-title: Comptes Rendus
– ident: 53
  doi: 10.1007/BF01207363
– ident: 90
  doi: 10.1016/j.jat.2009.11.002
– ident: 89
  doi: 10.1007/BF01180560
– ident: 63
  doi: 10.1016/0375-9601(93)90137-O
– volume: 34
  start-page: 9533
  issn: 0305-4470
  year: 2001
  ident: 99
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/34/44/313
– ident: 27
  doi: 10.1093/qmath/6.1.121
– ident: 44
  doi: 10.1016/S0377-0427(99)00090-4
– ident: 42
  doi: 10.1016/0022-247X(69)90037-7
– ident: 65
  doi: 10.1016/S0370-2693(01)00250-7
– ident: 93
  doi: 10.1007/s12043-009-0126-4
– ident: 114
  doi: 10.1007/BF01614245
– ident: 12
  doi: 10.2991/jnmp.2005.12.s1.41
– ident: 94
  doi: 10.1016/0377-0427(95)00262-6
– ident: 56
  doi: 10.1063/1.531122
– ident: 46
  doi: 10.1007/BF00760860
– ident: 54
  doi: 10.1063/1.530498
– volume: 6
  start-page: 57
  year: 1993
  ident: 83
  publication-title: Symmetries in Science
  doi: 10.1007/978-1-4899-1219-0_5
– ident: 22
  doi: 10.2991/jnmp.2008.15.s3.36
– ident: 113
  doi: 10.1007/BF02785163
– ident: 21
  doi: 10.1143/PTP.119.663
– ident: 35
  doi: 10.1007/BF01015906
– volume: 37
  start-page: 469
  issn: 0305-4470
  year: 2004
  ident: 115
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/37/2/015
– ident: 71
  doi: 10.1103/PhysRevLett.41.207
– volume: 48
  year: 2007
  ident: 16
  publication-title: J. Math. Phys.
– ident: 49
  doi: 10.1016/0001-8708(75)90151-6
– volume: 34
  start-page: 5653
  issn: 0305-4470
  year: 2001
  ident: 45
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/34/28/303
– start-page: 470
  year: 1996
  ident: 57
  publication-title: Proc. 4th Wigner Symposium (Guadalajara, 1995)
– ident: 64
  doi: 10.1016/S0550-3213(01)00389-3
– year: 2011
  ident: 102
– year: 1991
  ident: 2
  publication-title: Classical Orthogonal Polynomials of a Discrete Variable
  doi: 10.1007/978-3-642-74748-9
– ident: 41
  doi: 10.1103/RevModPhys.23.21
– ident: 61
  doi: 10.1016/0550-3213(81)90006-7
– ident: 11
  doi: 10.1143/PTP.125.851
– ident: 48
  doi: 10.1103/PhysRevA.5.1372
– volume: 40
  start-page: 9311
  issn: 1751-8113
  year: 2007
  ident: 85
  publication-title: J. Phys. A: Math. Theor.
  doi: 10.1088/1751-8113/40/31/009
– volume: 48
  year: 2007
  ident: 17
  publication-title: J. Math. Phys.
– ident: 52
  doi: 10.1016/0003-4916(86)90097-7
– ident: 96
  doi: 10.1142/S0217751X90000374
– volume: 94
  start-page: 1456
  issn: 1620-7742
  year: 1882
  ident: 59
  publication-title: C. R. Acad. Sci.
– year: 1939
  ident: 111
  publication-title: Orthogonal Polynomials
  doi: 10.1090/coll/023
– volume: 51
  year: 2010
  ident: 36
  publication-title: J. Math. Phys.
– volume: 51
  year: 2010
  ident: 106
  publication-title: J. Math. Phys.
  doi: 10.1063/1.3339676
– ident: 50
  doi: 10.1143/PTP.103.463
– volume: 113
  start-page: 970
  year: 1957
  ident: 28
  publication-title: Dokl. Acad. Nauk. CCCP
– volume: 34
  start-page: 10335
  issn: 0305-4470
  year: 2001
  ident: 100
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/34/47/502
– volume: 47
  year: 2006
  ident: 14
  publication-title: J. Math. Phys.
  doi: 10.1063/1.2349485
– ident: 10
  doi: 10.1016/j.physletb.2009.10.078
– year: 1984
  ident: 33
  publication-title: Algebraic Combinatorics: I. Association Schemes
– ident: 88
  doi: 10.1112/plms/s1-16.1.245
– ident: 76
  doi: 10.1016/0375-9601(93)91182-5
– ident: 91
  doi: 10.1016/j.jmaa.2009.05.052
– ident: 7
  doi: 10.1016/j.physletb.2009.08.004
– ident: 4
  doi: 10.1017/CBO9780511526251
– ident: 79
  doi: 10.1016/S0375-9601(01)00249-3
– volume: 33
  start-page: 9033
  issn: 0305-4470
  year: 2000
  ident: 51
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/33/49/303
– year: 2005
  ident: 5
  publication-title: Classical and Quantum Orthogonal Polynomials in One Variable
  doi: 10.1017/CBO9781107325982
– volume: 37
  start-page: 8513
  issn: 0305-4470
  year: 2004
  ident: 81
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/37/35/008
– ident: 72
  doi: 10.1103/PhysRevD.20.1321
– year: 1978
  ident: 70
  publication-title: An Introduction to Orthogonal Polynomials
– volume: 30
  start-page: 7621
  issn: 0305-4470
  year: 1997
  ident: 43
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/30/21/030
– volume: 21
  start-page: L195
  issn: 0305-4470
  year: 1988
  ident: 31
  publication-title: J. Phys. A: Math. Gen.
  doi: 10.1088/0305-4470/21/4/002
SSID ssj0054092
Score 2.2653844
SecondaryResourceType review_article
Snippet A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding...
SourceID proquest
pascalfrancis
crossref
SourceType Aggregation Database
Index Database
Enrichment Source
StartPage 353001
SubjectTerms Algebra
Exact sciences and technology
Mathematical analysis
Physics
Pictures
Polynomials
Quantum mechanics
Schroedinger equation
Solution space
Symmetry
Title Discrete quantum mechanics
URI https://www.proquest.com/docview/1620041453
Volume 44
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1da9swFBVrx6AwxrauNN1WMthbcRJbH7Ufy9bSja4tJYG8CUmWodCmZUketl-_cy3LdchgXV-UICI7vkcfR9c69zL2WVa2KnKlktyWtbfKJoWpPIicE4fOSSsUqZF_nKvTifg-ldOHfHm1umRhB-73X3UlT0EVdcCVVLL_gWx7UVTgO_BFCYRRPgrjr9cY9GC9JI3E2nF7cOtJyBsPsK9zzuDHmA8OjoJOJ4ZsbQIGdFSNrfO1NM3xHdqdL1uHjJmbkPD66tey6zkgV2iRjDrORDCHNMnToAUd-G5dUC3HGTJEaGx6Aped-S7tLJwhcubalIxpjLwD8V6Ua0mg4LIu-KjxZaxEwj6_0CeTszM9Pp6ON9jzDFsAyk7x7eIyrrIgmnXC6_a6Uf2NDX1bNxRiyOUw3GWFeLy8N3PYsgrJS9bW4ZpcjF-zVw1C_aMA8Rv2zM_esheXAa1ttheB7jdA91ug37HJyfH4y2nSJLVIHLjCIuGVKDGvGmPUoS2lN2JUUkqAzLgKdJsrL6TDB_5_4QTorAXDdTCAlUZiuPEdtjm7m_ld1sdzZqWowMHKAhfNC6eySnqMECdJT91jMj6xdk3Ed0o8cqPrkwd5rslSmiylhdBc6mCpHhu27e5DzJN_tthfMWjbjN7rZ0qKHvsULawxf9FLKTPzd8u5ThWN6FRIvveI37xnWw89-QPbXPxc-o9ghQu7X3ePP4LDWIw
linkProvider IOP Publishing
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=Discrete+quantum+mechanics&rft.jtitle=Journal+of+physics.+A%2C+Mathematical+and+theoretical&rft.au=Odake%2C+Satoru&rft.au=Sasaki%2C+Ryu&rft.date=2011-09-02&rft.issn=1751-8113&rft.eissn=1751-8121&rft.volume=44&rft.issue=35&rft.spage=1&rft.epage=47&rft_id=info:doi/10.1088%2F1751-8113%2F44%2F35%2F353001&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1751-8113&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1751-8113&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1751-8113&client=summon