Application of Lie algebra to NMR spectroscopy

Progress in Nuclear Magnetic Resonance Spectroscopy

Volumn 34, Issue 1, 1999, Pages 1-69

  Kristensen, J H ^a,b   Bildsoe H ^a   Jakobsen, H J ^a   Nielsen, N C ^a  

^a AARHUS UNIVERSITY   (Denmark)

^b The College of William and Mary   (United States)

Author keywords

Density operator algebra; Lie algebra; Lie groups; NMR spectroscopy

Indexed keywords

EID: 0008050303     PISSN: 00796565     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0079-6565(98)00026-0     Document Type: Review

References (90)

1. W.P. Aue, E. Bartholdi, R.R. Ernst, J. Chem. Phys. 64 (1976) 2229.
2. K. Nagayama, A. Kumar, K. Wüthric, R.R. Ernst, J. Magn. Reson. 40 (1980) 321.
3. A. Bax, R. Freeman, J. Magn. Reson. 44 (1981) 542.
4. A.A. Maudsley, R.R. Ernst, Chem. Phys. Lett. 50 (1977) 368.
5. A. Wokaun, R.R. Ernst Chem. Phys. Lett. 52 (1977) 407.
6. G. Bodenhausen, Prog. Nucl. Magn. Reson. Spectrosc. 14 (1981) 137.
7. S.R. Hartmann, E.L. Hahn, Phys. Rev. 128 (1962) 2042.
8. G.A. Morris, R. Freeman, J. Am. Chem. Soc. 101 (1979) 760.
9. D.M. Doddrell, D.T. Pegg, M.R. Bendall, J. Magn. Reson. 48 (1982) 323.
10. H.Y. Carr, E.M. Purcell, Phys. Rev. 94 (1954) 630.
11. J.H. Davis, K.R. Jeffrey, M. Bloom, M.I. Valic, T.P. Higgs, Chem. Phys. Lett. 42 (1976) 390.
12. J. Jeener, P. Broekaert, Phys. Rev. 157 (1967) 232.
13. C. Schmidt, B. Blumich, H.W. Spiess, J. Magn. Reson. 79 (1988) 269.
14. E.R. Andrew, A. Bradbury, R.G. Eades, Nature 182 (1958) 1659.
15. I.J. Lowe, Phys. Rev. Lett. 2 (1959) 285.
16. U. Haeberlen, J.S. Waugh, Phys. Rev. 175 (1968) 453.
17. U. Fano, Rev. Mod. Phys. 29 (1957) 74.
18. K. Blum, Density Matrix Theory and Applications, Plenum Press, New York, 1981.
19. O.W. Sørensen, G.W. Eich, M.H. Levitt, G. Bodenhausen, R. R. Ernst, Prog. Nucl. Magn. Reson. Spectrosc. 16 (1983) 163.
20. S. Vega, A. Pines, J. Chem. Phys. 66 (1977) 5624.
21. A. Wokaun, R.R. Ernst, J. Chem. Phys. 67 (1977) 1752.
22. S. Vega, J. Chem. Phys. 68 (1978) 5518.
23. B.C. Sanctuary, Mol. Phys. 48 (1983) 1155.
24. B.C. Sanctuary, T.K. Halstead, P.A. Osment, Mol. Phys. 49 (1983) 753.
25. B.C. Sanctuary, J. Magn. Reson. 61 (1985) 116.
26. G.J. Bowden, W.D. Hutchison, J. Magn. Reson. 67 (1986) 403.
27. G.J. Bowden, W.D. Hutchison, J. Khachan, J. Magn. Reson. 67 (1986) 415.
28. J.H. Kristensen, Advanced Concepts in Deuterium MAS NMR Spectroscopy, Ph.D. Thesis, Department of Chemistry, University of Aarhus, 1995.
29. N. Jacobson, Lie Algebras, Wiley, New York, 1962.
30. M. Hamermesh, Group Theory and Its Application to Physical Problems, Addison-Wesley, MA, 1962.
31. W. Miller, Symmetry Groups and Their Applications, Academic Press, New York, 1972.
32. B.G. Weybourne, Classical Groups for Physicists, Wiley, New York, 1974.
33. R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications, Wiley, New York, 1974.
34. P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, Oxford, 1958.
35. A. Messiah, Quantum Mechanics, Wiley, New York, 1961.
36. C.P. Slichter, Principles of Magnetic Resonance, Springer-Verlag, Berlin, 1990.
37. R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford University Press, Oxford, 1987.
38. J. Jeener, Adv. Magn. Reson. 10 (1982) 2.
39. W. Magnus, Comm. Pure Appl. Math. 7 (1954) 649.
40. R.M. Wilcox, J. Math. Phys. 8 (1967) 962.
41. A.M. Portis, Phys. Rev. 91 (1953) 1971.
42. E. Cartan, Bull. Soc. Math, de France 41 (1913) 53.
43. E. Cartan, Oeuvres Complétes, Gauthiers-Willars, Paris, 1952.
44. H. Weyl, Z. Math. 23 (1925) 271.
45. H. Weyl, Z. Math. 24 (1926) 328, 377, 789.
46. H. Weyl, Selecta, Birkhauser-Verlag, Basel, 1956.
47. E.B. Dynkin, Am. Math. Soc. Trans. Ser. 1 9 (1962) 308.
48. E.B. Dynkin, Am. Math. Soc. Trans. Ser. 2 6 (1965) 111, 245.
49. B.L. van der Waerden, Die Gruppentheoretische Methode in der Quantenmekanik, Springer-Verlag, Berlin, 1932.
50. B.L. van der Waerden, Z. Math. 37 (1933) 446.
51. G. Racah, Phys. Rev. 61 (1942) 186.
52. G. Racah, Phys. Rev. 62 (1942) 438.
53. G. Racah, Phys. Rev. 63 (1943) 367.
54. G. Racah, Phys. Rev. 76 (1949) 1352.
55. G. Racah, Ergeb. Exakt. Naturwis. 37 (1965) 28.
56. R.E. Behrends, J. Dreitlein, C. Fronsdal, W. Lee, Rev. Mod. Phys. 34 (1962) 1.
57. H. Casimir, Proc. R. Acad. Amstd. 34 (1931) 844.
58. M.E. Rose, Elementary Theory of Angular Momentum, Wiley, New York, 1957.
59. A.R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, 1957.
60. D.M. Brink, G.R. Satchler, Angular Momentum, Oxford University Press, Oxford, 1962.
61. M. Tinkham, Group Theory and Quantum Mechanics, McGraw-Hill, New York, 1964.
62. P. Diehl, R.K. Harris, R.G. Jones, Prog. Nucl. Magn. Reson. Spectrosc. 3 (1967) 1.
63. R.A. Hoffmann, S. Forsén, B. Gestblom, NMR Basic Principles and Progress 5 (1971) 1.
64. C. Eckart, Rev. Mod. Phys. 2 (1930) 302.
65. E.P. Wigner, Group Theory, Academic Press, New York, 1959.
66. G.F. Koster, Phys. Rev. 109 (1958) 227.
67. A.P. Stone, Proc. Camb. Philos. Soc. 57 (1961) 460.
68. L. O'Raifeartaigh, in: Group Theory and its Applications, Vol. I, Academic Press, New York, 1968.
69. R.E. Behrends, in: Group Theory and its Applications, Vol. I, Academic Press, New York, 1968.
70. A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, Oxford, 1961.
71. U. Haeberlen, High Resolution NMR in Solids Adv. Magn. Reson. Suppl. 1, Academic Press, New York, 1976.
72. H.W. Spiess, NMR Basic Principles and Progress 15 (1978) 55.
73. M. Mehring, High Resolution NMR Spectroscopy in Solids, Springer-Verlag, Berlin, 1983.
74. J.L. Ackerman, R. Eckman, A. Pines, Chem. Phys. 42 (1979) 423.
75. R. Eckman, M. Alia, A. Pines, J. Magn. Reson. 41 (1980) 440.
76. N.J. Clayden, Chem. Phys. Lett. 131 (1986) 517.
77. J.H. Kristensen, H. Bildsøe, H.J. Jakobsen, N.C. Nielsen, J. Magn. Reson. 92 (1991) 443.
78. A.J. Kim, L.G. Butler, J. Magn. Reson. 99 (1992) 292.
79. R. Poupko, Z. Olender, D. Reichert, Z. Luz, J. Magn. Reson. 106(1994) 113.
80. T. Chiba, J. Chem. Phys. 41 (1964) 1352.
81. M.J. Hunt, A.L. Mackay, J. Magn. Reson. 15 (1974) 402.
82. B. Berglund, R.W. Waughan, J. Chem. Phys. 73 (1980) 2037.
83. J.H. Kristensen, H. Bildsøe, H.J. Jakobsen, N.C. Nielsen, J. Magn. Reson. 100 (1992) 437.
84. R.J. Schadt, R.Y. Dong, E. Günther, B. Blümich, J. Magn. Reson. 96 (1992) 393.
85. M.M. Maricq, J.S. Waugh, J. Chem. Phys. 70 (1979) 3300.
86. A. Samoson, E. Kundla, E. Lippmaa, J. Magn. Reson. 49 (1982) 350.
87. A.D. Bain, J. Magn. Reson. 56 (1984) 418.
88. G. Bodenhausen, H. Kogler, R.R. Ernst, J. Magn. Reson. 58 (1984) 370.
89. M. Bloom, J.H. Davis, M.I. Valic, Can. J. Phys. 58 (1980) 1510.
90. M. Munowitz, J. Magn. Reson. 73 (1987) 338.