Two Theoretical Approaches in Solid-State Nuclear Magnetic Resonance Spectroscopy
Author(s)
Eugene Stephane Mananga*
ABSTRACT
We present the theories used in solid-state nuclear magnetic resonance and the expansion schemes used as numerical integrators for solving the time dependent Schrodinger Equation. We highlight potential future theoretical and numerical directions in solid-state nuclear magnetic resonancesuch as the Chebychev expansion and the transformation of Cayley.
Cite this paper
Mananga, E. (2014) Two Theoretical Approaches in Solid-State Nuclear Magnetic Resonance Spectroscopy. Journal of Modern Physics, 5, 458-463. doi: 10.4236/jmp.2014.56055.
Mananga, E. (2014) Two Theoretical Approaches in Solid-State Nuclear Magnetic Resonance Spectroscopy. Journal of Modern Physics, 5, 458-463. doi: 10.4236/jmp.2014.56055.
References
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http://dx.doi.org/10.1073/pnas.152346599 [8] Ernst, R.R., Bodenhausen, G. and Wokaun, A. (1987) Clarendon. Oxford. [9] Mananga, E.S., Roopchand, R., Rumala, Y.S. and Boutis, G.S. (2007) Journal of Magnetic Resonance, 185, 28.
http://dx.doi.org/10.1016/j.jmr.2006.10.016 [10] Mananga, E.S., Rumala, Y.S. and Boutis, G.S. (2006) Journal of Magnetic Resonance, 181, 296.
http://dx.doi.org/10.1016/j.jmr.2006.05.015 [11] Rhim, W.-K., Pines, A. and Waugh, J.S. (1971) Physical Review B, 3, 684. http://dx.doi.org/10.1103/PhysRevB.3.684 [12] Eden, M. and Levitt, M.H. (1999) Journal of Chemical Physics, 111, 1511. http://dx.doi.org/10.1063/1.479410 [13] Carravetta, M., Eden, M., Zhao, X., Brinkmann, A. and Levitt, M.H. (2000) Chemical Physical Letters, 321, 205.
http://dx.doi.org/10.1016/S0009-2614(00)00340-7 [14] Levitt, M.H. (2008) Journal of Chemical Physics, 128, 052205. http://dx.doi.org/10.1063/1.2831927 [15] Tycko, R. (1990) Journal of Chemical Physics, 92, 5776. http://dx.doi.org/10.1063/1.458398 [16] Vega, S. and Pines, A. (1977) Journal of Chemical Physics, 66, 5624. http://dx.doi.org/10.1063/1.433884 [17] Haeberlen, U. and Waugh, J.S. (1968) Physical Review, 175, 453. http://dx.doi.org/10.1103/PhysRev.175.453 [18] Shirley, J.H. (1965) Physical Review B, 138, 979. http://dx.doi.org/10.1103/PhysRev.138.B979 [19] Maricq, M.M. (1982) Physical Review B, 25, 6622. http://dx.doi.org/10.1103/PhysRevB.25.6622 [20] Zur, Y., Levitt, M.H. and Vega, S. (1983) Journal of Chemical Physics, 78, 5293. http://dx.doi.org/10.1063/1.445483 [21] Fer, F. (1958) Bulletin de la Classe des Sciences, Academie Royale de Belgique, 44, 818. [22] Mananga, E.S. and Charpentier, T. (2011) Journal of Chemical Physics, 135, Article ID: 044109.
http://dx.doi.org/10.1063/1.3610943 [23] Magnus, W. (1954) Communications on Pure and Applied Mathematics, 7, 649-673.
http://dx.doi.org/10.1002/cpa.3160070404 [24] Dumont, R.S., Jain, S. and Bain, A. (1997) Journal of Chemical Physics, 106, 5928.
http://dx.doi.org/10.1063/1.473258 [25] Tal-Ezer, H. and Kosloff, R. (1984) Journal of Chemical Physics, 81, 3967. http://dx.doi.org/10.1063/1.448136 [26] Rivlin, T.J. (1990) Chebychev Polynomials. 2nd Edition, Wiley, New York, 188. [27] Blanes, S., Casas, F., Oteo, J.A. and Ros, J. (2009) Physics Reports, 470, 151-238.
http://dx.doi.org/10.1016/j.physrep.2008.11.001 [28] Blanes, S., Casas, F. and Ros, J. (2002) BIT Numerical Mathematics, 42, 262-284.
http://dx.doi.org/10.1023/A:1021942823832 [29] Moler, C.B. and Van Loan, C.F. (2003) SIAM Review, 45, 3-49. [30] Nettesheim, P. (2000) Mixed Quantum-Classical Dynamics: A Unified Approach to Mathematical Modelling and Numerical Simulation. Ph.D. Thesis, Freie Universitat Berlin, Berlin. [31] Iserles, A. (2001) Foundations of Computational Mathematics, 1, 129-160. http://dx.doi.org/10.1007/s102080010003 [32] Süli, E. and Mayers, D. (2003) An Introduction to Numerical Analysis. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511801181 [33] Zou, C.W. and Shi, J.L. (2009) Nonlinear Analysis, 71, 1100-1107. http://dx.doi.org/10.1016/j.na.2008.11.033 [34] Lopez, L. and Politi, T. (2001) Applied Numerical Mathematics, 36, 35-55.
http://dx.doi.org/10.1016/S0168-9274(99)00049-5 [35] Leimkuhler, J.B. and Van Vleck, E.S. (1997) Numerische Mathematik, 77, 269-282.
http://dx.doi.org/10.1007/s002110050286 [36] Chu, M.T. and Morris, L.K. (1988) SIAM Journal on Numerical Analysis, 25, 1383-1391.
http://dx.doi.org/10.1137/0725080 [37] Mananga, E.S., Reid, A.E. and Charpentier, T. (2012) Solid State Nuclear Magnetic Resonance, 41, 32-47.
http://dx.doi.org/10.1016/j.ssnmr.2011.11.004 [38] Leskes, M., Madhu, P.K. and Vega, S. (2010) Progress in Nuclear Magnetic Resonance Spectroscopy, 57, 345-380.
http://dx.doi.org/10.1016/j.pnmrs.2010.06.002 [39] Scholz, I., Van Beek, J.D. and Ernst, M. (2010) Solid State Nuclear Magnetic Resonance, 37, 39-59.
http://dx.doi.org/10.1016/j.ssnmr.2010.04.003
[1] Schrodinger, E. (1926) Physical Reviews, 28, 1049-1070. http://dx.doi.org/10.1103/PhysRev.28.1049 [2] Dirac, P.A.M. (1958) Theprinciples of Quantum Mechanics. 4th Edition, Oxford University Press, Oxford. [3] Hazewinkel, M. (2001) Schrodinger Equation. Encyclopedia of Mathematics, Springer. [4] Müller-Kirsten, H.J.W. (2012) Introduction to Quantum Mechanics: Schrodinger Equation and Path Integral. 2nd Edititon, World Scientific. http://dx.doi.org/10.1142/8428 [5] Griffiths, D.J. (2004) Introduction to Quantum Mechanics. 2nd Edition, Benjamin Cummings. [6] Vandersypen, L.M.K. and Chuang, I.L. (2004) Reviews of Modern Physics, 76, 1034. [7] Rienstra, C.M., Tucker-Kellogg, L., Jaroniec, C.P., Hohwy, M., Reif, B., McMahon, M.T., Tidor, B., Lozano-Perez, T. and Griffin, R.G. (2002) Proceedings of National Academy Science of the USA, 99, 10260.
http://dx.doi.org/10.1073/pnas.152346599 [8] Ernst, R.R., Bodenhausen, G. and Wokaun, A. (1987) Clarendon. Oxford. [9] Mananga, E.S., Roopchand, R., Rumala, Y.S. and Boutis, G.S. (2007) Journal of Magnetic Resonance, 185, 28.
http://dx.doi.org/10.1016/j.jmr.2006.10.016 [10] Mananga, E.S., Rumala, Y.S. and Boutis, G.S. (2006) Journal of Magnetic Resonance, 181, 296.
http://dx.doi.org/10.1016/j.jmr.2006.05.015 [11] Rhim, W.-K., Pines, A. and Waugh, J.S. (1971) Physical Review B, 3, 684. http://dx.doi.org/10.1103/PhysRevB.3.684 [12] Eden, M. and Levitt, M.H. (1999) Journal of Chemical Physics, 111, 1511. http://dx.doi.org/10.1063/1.479410 [13] Carravetta, M., Eden, M., Zhao, X., Brinkmann, A. and Levitt, M.H. (2000) Chemical Physical Letters, 321, 205.
http://dx.doi.org/10.1016/S0009-2614(00)00340-7 [14] Levitt, M.H. (2008) Journal of Chemical Physics, 128, 052205. http://dx.doi.org/10.1063/1.2831927 [15] Tycko, R. (1990) Journal of Chemical Physics, 92, 5776. http://dx.doi.org/10.1063/1.458398 [16] Vega, S. and Pines, A. (1977) Journal of Chemical Physics, 66, 5624. http://dx.doi.org/10.1063/1.433884 [17] Haeberlen, U. and Waugh, J.S. (1968) Physical Review, 175, 453. http://dx.doi.org/10.1103/PhysRev.175.453 [18] Shirley, J.H. (1965) Physical Review B, 138, 979. http://dx.doi.org/10.1103/PhysRev.138.B979 [19] Maricq, M.M. (1982) Physical Review B, 25, 6622. http://dx.doi.org/10.1103/PhysRevB.25.6622 [20] Zur, Y., Levitt, M.H. and Vega, S. (1983) Journal of Chemical Physics, 78, 5293. http://dx.doi.org/10.1063/1.445483 [21] Fer, F. (1958) Bulletin de la Classe des Sciences, Academie Royale de Belgique, 44, 818. [22] Mananga, E.S. and Charpentier, T. (2011) Journal of Chemical Physics, 135, Article ID: 044109.
http://dx.doi.org/10.1063/1.3610943 [23] Magnus, W. (1954) Communications on Pure and Applied Mathematics, 7, 649-673.
http://dx.doi.org/10.1002/cpa.3160070404 [24] Dumont, R.S., Jain, S. and Bain, A. (1997) Journal of Chemical Physics, 106, 5928.
http://dx.doi.org/10.1063/1.473258 [25] Tal-Ezer, H. and Kosloff, R. (1984) Journal of Chemical Physics, 81, 3967. http://dx.doi.org/10.1063/1.448136 [26] Rivlin, T.J. (1990) Chebychev Polynomials. 2nd Edition, Wiley, New York, 188. [27] Blanes, S., Casas, F., Oteo, J.A. and Ros, J. (2009) Physics Reports, 470, 151-238.
http://dx.doi.org/10.1016/j.physrep.2008.11.001 [28] Blanes, S., Casas, F. and Ros, J. (2002) BIT Numerical Mathematics, 42, 262-284.
http://dx.doi.org/10.1023/A:1021942823832 [29] Moler, C.B. and Van Loan, C.F. (2003) SIAM Review, 45, 3-49. [30] Nettesheim, P. (2000) Mixed Quantum-Classical Dynamics: A Unified Approach to Mathematical Modelling and Numerical Simulation. Ph.D. Thesis, Freie Universitat Berlin, Berlin. [31] Iserles, A. (2001) Foundations of Computational Mathematics, 1, 129-160. http://dx.doi.org/10.1007/s102080010003 [32] Süli, E. and Mayers, D. (2003) An Introduction to Numerical Analysis. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511801181 [33] Zou, C.W. and Shi, J.L. (2009) Nonlinear Analysis, 71, 1100-1107. http://dx.doi.org/10.1016/j.na.2008.11.033 [34] Lopez, L. and Politi, T. (2001) Applied Numerical Mathematics, 36, 35-55.
http://dx.doi.org/10.1016/S0168-9274(99)00049-5 [35] Leimkuhler, J.B. and Van Vleck, E.S. (1997) Numerische Mathematik, 77, 269-282.
http://dx.doi.org/10.1007/s002110050286 [36] Chu, M.T. and Morris, L.K. (1988) SIAM Journal on Numerical Analysis, 25, 1383-1391.
http://dx.doi.org/10.1137/0725080 [37] Mananga, E.S., Reid, A.E. and Charpentier, T. (2012) Solid State Nuclear Magnetic Resonance, 41, 32-47.
http://dx.doi.org/10.1016/j.ssnmr.2011.11.004 [38] Leskes, M., Madhu, P.K. and Vega, S. (2010) Progress in Nuclear Magnetic Resonance Spectroscopy, 57, 345-380.
http://dx.doi.org/10.1016/j.pnmrs.2010.06.002 [39] Scholz, I., Van Beek, J.D. and Ernst, M. (2010) Solid State Nuclear Magnetic Resonance, 37, 39-59.
http://dx.doi.org/10.1016/j.ssnmr.2010.04.003