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Evolution operator equations: Integration with algebraic and finitedifference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory

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References

  1. Dattoli G., Gallardo J. C. andTorre A.,Riv. Nuovo Cimento,1 (1988) 11.

    MathSciNet  Google Scholar 

  2. Srivastava H. M. andManocha H. L.,A Treatise on Generating Functions (Ellis-Horwood Limited, New York) 1984, Chapt. 6;Chu P. M.,Lie Groups (Cambridge University Press, London, New York) 1957;Helgason S.,Differential Geometry and Symmetric Spaces (Academic Press, New York) 1962;Gaggenhaimer H. W.,Differential Geometry (McGraw-Hill, New York) 1963;Miller W. jr.,Lie Theory and Special Functions (Academic Press, New York) 1968.

    MATH  Google Scholar 

  3. Wilcox R. M.,J. Math. Phys.,8 (1967) 962.

    Article  ADS  MathSciNet  Google Scholar 

  4. Sack R.,Philos. Mag.,3 (1958) 497.

    Article  ADS  MathSciNet  Google Scholar 

  5. Berry M. V.,The Light Diffraction by Ultrasounds (Academic Press, London) 1966.

    Google Scholar 

  6. Aldaya V., Bisquert J. andNavarro-Salas J.,Phys. Lett. A,156 (1991) 381;Zarzo A. andMartinez A.,J. Math. Phys.,34 (1993) 2926;Nagel B.,J. Math. Phys.,35 (1994) 1549.

    Article  ADS  MathSciNet  Google Scholar 

  7. Hausdorff F.,Ber. Verh. Saechs. Akad. Wiss Leipzig Math. Naturw. K1,58 (1906) 135;Frölich J.,Commun. Math. Phys.,54 (1977) 135;Brittin W. andWyss W.,Commun. Math. Phys.,49 (1976) 109.

    Google Scholar 

  8. Crofton M. W.,Q. J. Math.,15 (1979) 323.

    Google Scholar 

  9. Smirnov Y. andTurbiner A.,Mod. Phys. Lett. A,10 (1995) 1795.

    Article  ADS  MathSciNet  Google Scholar 

  10. Burchnall J. S.,Q. J. Math.,12 (1941) 9.

    Article  ADS  MathSciNet  Google Scholar 

  11. Appell P. andKampè de Feriet J.,Fonctions Hypergeometriques and Hyperspheriques. PolynOmes d’Hermite (Gauthiers-Villars, Paris) 1926.

    MATH  Google Scholar 

  12. Gould H. W. andHopper A. T.,Duke Math. J.,29 (1962) 51.

    Article  MathSciNet  Google Scholar 

  13. Nieto M. M. andTruax D. R., quant-ph./9506008, LA-UR 95–1772.

  14. Hermite Ch.,C. R. Acad. Sci,58 (1864) 93.

    Google Scholar 

  15. Dattoli G. andTorre A.,Theory and Application of Generalized Bessel Functions (Aracne, Rome) 1996.

    Google Scholar 

  16. Wei J. andNorman E.,J. Math. Phys.,4 (1963) 575.

    Article  ADS  MathSciNet  Google Scholar 

  17. Dattoli G., Richetta M., Schettini G. andTorre A.,J. Math. Phys.,31 (1990) 2856.

    Article  ADS  MathSciNet  Google Scholar 

  18. Goldstein H.,Classical Mechanics (Addison Wesley, Reading, Mass.) 1959.

    MATH  Google Scholar 

  19. Dragt A. J. andFinn J. M.,J. Math. Phys.,17 (1976) 2215.

    Article  ADS  MathSciNet  Google Scholar 

  20. Namias V.,J. Inst. Math. Its Apll,25 (1980) 241.

    Article  MathSciNet  Google Scholar 

  21. Dattoli G., Torre A. andMazzacurati G.,Nuovo Cimento B,112 (1997) 133.

    Google Scholar 

  22. Dattoli G., Mari C. andTorre A.,Nuovo Cimento B,106 (1991) 201;Dattoli G. andTorre A.,J. Math. Phys.,34 (1995) 5062.

    ADS  MathSciNet  Google Scholar 

  23. Bender C. M. andSharp D. H.,Phys. Rev. Lett,50 (1983) 1535;Bender C. M.,Milton K. A. andSharp D. H.,Phys. Rev. Lett.,51 (1983) 1815.

    Article  ADS  MathSciNet  Google Scholar 

  24. Moncrief V.,Phys. Rev. D,28 (1983) 2485.

    Article  ADS  MathSciNet  Google Scholar 

  25. Vazquez L.,Z. Naturforsch. A,41a (1986) 788;42a (1987) 905.

    ADS  Google Scholar 

  26. Dattoli G., Ottaviani P. L., Segreto A. andTorre A.,Nuovo Cimento B,111 (1996) 825.

    Article  ADS  Google Scholar 

  27. Dattoli G., Giannessi L., Ottaviani P. L. andTorre A.,Phys. Rev. E,51 (1995) 821.

    Article  ADS  Google Scholar 

  28. Dragt A. J.,Phys. Rev. Lett,75 (1995) 1946.

    Article  ADS  Google Scholar 

  29. Vazquez L.,Phys. Rev. D,35 (1987) 3274.0

    Article  ADS  Google Scholar 

  30. Sanchez A. andVázquez L.,Int. J. Mod. Phys. B,5 (1991) 2825.

    Article  ADS  Google Scholar 

  31. Konotop V. V. andVázquez L.,Non Linear Random Waves (World Sci. Publ. Co., Singapore) 1994.

    Book  MATH  Google Scholar 

  32. Dyson F. J.,Phys. Rev.,75 (1949) 486.

    Article  ADS  MathSciNet  Google Scholar 

  33. Feynman R. P.,Quantum Electrodynamics (Benjamin, New York) 1961.

    MATH  Google Scholar 

  34. Magnus W.,Commun. Pure Appl. Math.,7 (1954) 649;Pechukas P. andLight J. C.,J. Chem. Phys.,44 (1966) 3897.

    Article  MathSciNet  Google Scholar 

  35. Feit M. D., Fleck. J. A. jr. andSteiger A.,J. Comput Phys.,47 (1982) 412;Feit M. D.,Fleck J. A. jr. andSteiger A.,J. Chem. Phys.,78 (1982) 301;Feit M. D.,Fleck J. A. jr. andSteiger A.,J. Chem. Phys.,80 (1984) 2578.

    Article  ADS  MathSciNet  Google Scholar 

  36. Torres-Vega Go. andFrederick J. H.,Phys. Rev. Lett,67 (1991) 2601.

    Article  ADS  Google Scholar 

  37. Jimenez S. andVázquez L.,Appl. Math. Comput.,35 (1990) 61.

    MathSciNet  Google Scholar 

  38. Zhang Fei, Perez-Garcia V. M. andVazquez L.,Appl. Math. Comput,71 (1995) 165.

    MathSciNet  Google Scholar 

  39. Feng K. andQin M.,Lect. Notes Math.,1297 (1987) 1–37.

    Article  MathSciNet  Google Scholar 

  40. Scovel C., inThe Geometry of Hamiltonian Systems, edited byT. Ratiu (Springer-Verlag, Berlin) 1991.

    Google Scholar 

  41. Sanz-Serna J. M.,BIT,28 (1988) 877.

    Article  MathSciNet  Google Scholar 

  42. Ruth R. D.,IEEE Trans. Nucl. Sci,NS-30 (1983) 2669.

    Article  ADS  Google Scholar 

  43. Kinoshita H., Yoshida H. andNakai H.,Celest Mech,50 (1991) 59.

    Article  ADS  Google Scholar 

  44. Forest E. andRuth R. D.,Physica D,43 (1990) 105.

    Article  ADS  MathSciNet  Google Scholar 

  45. Dragt A. J. andFinn J. M.,J. Math. Phys.,17 (1976) 2215.

    Article  ADS  MathSciNet  Google Scholar 

  46. Yoshida H.,Celest. Mech,56 (1993) 27.

    Article  ADS  Google Scholar 

  47. Yoshida H., unpublished and ref.Celest. Mech,56 (1993) 27.

  48. Vázquez L.,Phys. Rev. D,34 (1986) 3253.

    Article  ADS  Google Scholar 

  49. Vázquez L.,Phys. Rev. D,32 (1985) 2066.

    Article  ADS  MathSciNet  Google Scholar 

  50. Dattoli G.,Quattromini M.,Torre A. andOttaviani P. L.,Proc. Euroconference: Supercomputation in Nonlinear and Disordered Systems: Algorithms, Applications and Architectures, September 23–28, 1996, San Lorenzo de El Escorial, Madrid, Spain, edited byL. Vázquez,F.Tirado andI. Martin (World Sci. Publ.) 1997, in press;Dattoli G.,Giannessi L.,Quattromini M. andTorre A.,Proc. Euroconference: Supercomputation in Nonlinear and Disordered Systems: Algorithms, Applications and Architectures, September 23–28, 1996, San Lorenzo de El Escorial, Madrid, Spain, edited byL. Vázquez,F. Tirado andI. Martin (World Sci. Publ.) 1997, in press;Dattoli G.,Giannessi L.,Quattromini M. andTorre A., submitted for publication.

  51. Suzuki M.,Phys. Lett. A,146 (1990) 319;Suzuki M.,J. Math. Phys.,32 (1991) 400.

    Article  ADS  MathSciNet  Google Scholar 

  52. Yoshida H.,Phys. Lett. A,150 (1990) 262.

    Article  ADS  MathSciNet  Google Scholar 

  53. Dattoli G.,Giannessi L.,Ottaviani P. L.,Quattromini M. andMarranca A., submitted for publication;Dattoli G.,Quattromini M.?,Torre A. andVázquez L., submitted for publication.

  54. Guillemin V. andSternberg S.,Symplectic Techniques in Physics (Cambridge Univ. Press, New York, N.Y.) 1990.

    MATH  Google Scholar 

  55. Lie Methods in Optics, Proceedings of the Leon Conference 1985, edited byJ. Sanchez Mondragon andK. B. Wolf (Springer-Verlag, Berlin) 1986.

    MATH  Google Scholar 

  56. Leontovich M. andFock V.,Sov. J. Phys.,10 (1946) 13.

    MathSciNet  Google Scholar 

  57. Dattoli G.,Giannessi L.,Ottaviani P. L. andQuattromini M., submitted for publication.

  58. Lawson J. D.,The Physics of Charged Beams (Clarendon Press, Oxford) 1978.

    Google Scholar 

  59. Dattoli G. andTorre A., inDynamical Symmetries and Chaotic Behavior in Physical Systems, edited byG. Maino, L. Fronzoni andM. Pettini (World-Scientific Publ. Co., Singapore) 1991, pp. 21–89.

    Google Scholar 

  60. Bender C. M., Milton K. A. andSharp D. H.,Phys. Rev. D,31 (1985) 383.

    Article  ADS  MathSciNet  Google Scholar 

  61. Bender C. M., Cooper F., O’Dell J. E. andSimmons L. M. jr.,Phys. Rev. Lett,55 (1985) 901.

    Article  ADS  MathSciNet  Google Scholar 

  62. Bender C. M., Milton K. A., Sharp D. H., Simmons L. M. jr. andStong R.,Phys. Rev. D,32 (1985) 1476.

    Article  ADS  MathSciNet  Google Scholar 

  63. Bender C. M. andMilton K. A.,Phys. Rev. D,34 (1986) 3149.

    Article  ADS  MathSciNet  Google Scholar 

  64. Vázquez L.,Rev. R. Acad. Cienc. Exactas, Fis. Nat. Madrid,LXXIX (1985) 661.

    Google Scholar 

  65. Vázquez L.,About the unitary discretizations of Heisenberg equations of motion, BiBoS 233/86 (Bielefeld University).

  66. Vázquez L.,Phys. Rev. D,35 (1987) 1409.

    Article  ADS  MathSciNet  Google Scholar 

  67. Vázquez L.,Contributions to Nonlinear Partial Differential Equations, edited byJ. I. Diaz andP. L. Lions (Longman Scientific and Technical) 1987, p. 267.

  68. Rodriguez M. J. andVázquez L.,Nonlinear Semigroups, Partial Differential Equations and Attractors, Lect Notes Math.,1394, edited byT. L. Gill andW. W. Zachary (Springer-Verlag, Berlin) 1987, p. 131.

    Google Scholar 

  69. Streit L.,Vázquez L., andVilela Mendes R.,Essays on Classical and Quantum Dynamics, edited byJ. A. Ellison andH. Überall (Gordon and Breach Science Publishers) 1991, p. 129.

  70. Vázquez L.,Rev. Esp. Fis.,4 (1990) 63.

    Google Scholar 

  71. Qin Meng-Zhao andZhang Mei-Qing:J. Statist. Phys.,60 (1990) 839.

    Article  ADS  MathSciNet  Google Scholar 

  72. Vázquez L.,Phys. Lett,144 (1990) 15.

    Article  Google Scholar 

  73. Strauss W. A. andVázquez L.,J. Comput Phys.,28 (1978) 271.

    Article  ADS  MathSciNet  Google Scholar 

  74. Vázquez L.,Numerical solutions of the equation Ü + U p = 0, Preprint Brown University (1977).

  75. Vázquez L.,An. Fis. A,83 (1987) 254.

    Google Scholar 

  76. Greenspan D.,J. Comput. Phys.,56 (1984) 28.

    Article  ADS  MathSciNet  Google Scholar 

  77. Delfour M., Fortin M. andPayre G.,J. Comput. Phys.,44 (1981) 277.

    Article  ADS  MathSciNet  Google Scholar 

  78. Dias de Deus J., Henriques A. B. andPulido J. M. R.,Z. Phys. C,7 (1981) 157.

    Article  ADS  Google Scholar 

  79. Dias de Deus J.,Phys. Rev. D,26 (1982) 2782.

    Article  ADS  Google Scholar 

  80. Dias de Deus J. andHenriques A. B.,Port. Phys.,16 (1985) 105.

    Google Scholar 

  81. Chang Y. F., Tabor M. andWeiss J.,J. Math. Phys.,23 (1982) 531.

    Article  ADS  MathSciNet  Google Scholar 

  82. Grammaticos B., Dorizzi B. andRamani A.,J. Math. Phys.,24 (1983) 2289.

    Article  ADS  MathSciNet  Google Scholar 

  83. Casati G., Chirikov B. V., Guarnieri I. andShepelyanky D. L.,Phys. Rev. Lett,56 (1986) 2437.

    Article  ADS  Google Scholar 

  84. Bardsley J. N., Bayfield J. E., Pinnaduwage L. A. andSundaram B.,Phys. Rev. Lett.,56 (1986) 1007.

    Article  ADS  Google Scholar 

  85. Holle A., Wiebusch G., Main J., Hager B., Rottke H. andWelge K. H.,Phys. Rev. Lett,56 (1986) 2594.

    Article  ADS  Google Scholar 

  86. Main J., Wiebusch G., Holle A. andWelge K. H.,Phys. Rev. Lett,57 (1986) 2789.

    Article  ADS  Google Scholar 

  87. Glimm J. andJaffee A.,Quantum Physics: A Functional Integral Point of View (Springer-Verlag, Berlin) 1981.

    Book  Google Scholar 

  88. Creutz M.,Quarks, Gluons and Lattices (Cambridge University Press) 1983.

  89. Dashen R. F., Hasslacher B. andNeveu A.,Phys. Rev. D,11 (1975) 3424.

    Article  ADS  MathSciNet  Google Scholar 

  90. Milton K. A.,Lett. Math. Phys.,34 (1995) 285.

    Article  ADS  MathSciNet  Google Scholar 

  91. Nieto M. M. andTruax D. R.,Phys. Lett. A,208 (1995) 8.

    Article  ADS  MathSciNet  Google Scholar 

  92. Dattoli G. andTorre A.,Proceedings of the Workshop on Special Functions, Pugnochiuso, 18–21 June 1997.

  93. Witschel W.,Phys. Lett A,111 (1985) 383.

    Article  ADS  MathSciNet  Google Scholar 

  94. Bell E. T.,Ann. Math.,35 (1934) 258.

    Article  Google Scholar 

  95. See,e.g.,Abramowitz M. andStegun I. A.,Handbook of Mathematical Functions (Dover Pub. Inc., New York) 1972.

    MATH  Google Scholar 

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Authors and Affiliations

  1. ENEA, Dipartimento Innovazione, Settore di Fisica Applicata, Centro Ricerche Frascati via E, Fermi 45, 00044, Frascati Roma, Italy

    G. Dattoli & A. Torre

  2. ENEA, Dipartimento Innovazione, Settore di Fisica Applicata, Centro Ricerche Bologna via Don Fiammelli 2, 40129, Bologna, Italy

    P. L. Ottaviani

  3. Departamento de Matemática Aplicada, Escuela Superior de Informática Universidad Complutense, 28040, Madrid, Spain

    L. Vázquez

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  1. G. Dattoli
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  3. A. Torre
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  4. L. Vázquez
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Dattoli, G., Ottaviani, P.L., Torre, A. et al. Evolution operator equations: Integration with algebraic and finitedifference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory. Riv. Nuovo Cim. 20, 3–133 (1997). https://doi.org/10.1007/BF02907529

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