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Rayleigh-Schrodinger Perturbation Theory (RSPT)

  • G. A. Arteca
  • F. M. Fernández
  • E. A. Castro
Part of the Lecture Notes in Chemistry book series (LNC, volume 53)

Abstract

We devote this Section to present RSPT in a way appropriate to our specific needs. There are several alternative manners to introduce this formalism which can be found in the standard literature /1–3/.

Keywords

Schrodinger Equation Anharmonic Oscillator Recurrence Relationship Ricatti Equation Perturbation Correction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References of Chapter III

  1. /1/.
    E. Merzbacher, Quantum Mechanics, Wiley and Sons, New York, 1970.Google Scholar
  2. /2/.
    L.I. Schiff, Quantum Mechanics, McGraw-Hill-Kogakusha, International Student Edition, Tokyo, 1968.Google Scholar
  3. /3/.
    L.D. Landau and E.M. Lifshits, Quantum Mechanics: Non-Relativistic Theory, Pergamon, London, 1953.Google Scholar
  4. /4/.
    A. Dalgarno and J.T. Lewis, Proc. R. Soc. London Ser. A 233 (1955) 70.CrossRefGoogle Scholar
  5. /5/.
    A. Dalgarno and J.T. Lewis, Proc. Phys. Soc. A 69 (1956) 623.Google Scholar
  6. /6/.
    A. Dalgarno and A.L. Stewart, Proc. R. Soc. London Ser. A 233 (1956) 269.Google Scholar
  7. /7/.
    A. Dalgarno and A.L. Stewart, Proc. R. Soc. London Ser. A 238 (1956) 276.CrossRefGoogle Scholar
  8. /8/.
    A. Dalgarno and N. Lynn, Proc. Phys. Soc. A 70 (1957) 223.CrossRefGoogle Scholar
  9. /9/.
    /9/ A. Dalgarno and A.L. Stewart, Proc. R. Soc. London Ser. A 240 (1957) 274.CrossRefGoogle Scholar
  10. /10/.
    A. Dalgarno and J.T. Lewis, Proc. R. Soc. London Ser. A 247 (1953) 245.Google Scholar
  11. /12/.
    A. Unsöld, Z. Physik 43 (1927) 563.CrossRefGoogle Scholar
  12. /13/.
    R.J. Swenson and S.H. Danforth, J. Chem. Phys, 57 (1972) 1734CrossRefGoogle Scholar
  13. /14/.
    J. Killingbeck, Phys. Lett. A 65 (1973) 37.Google Scholar
  14. /15/.
    M.F. Marziani, J. Phys. A 17 (1934) 547.CrossRefGoogle Scholar
  15. /16/.
    C.S. Lai and H.E. Lin, J.Phys. A 15 (1932) 1495.CrossRefGoogle Scholar
  16. /17/.
    M. Grant and C.S. Lai, Phys. Rev. A 20 (1979) 718.CrossRefGoogle Scholar
  17. /18/.
    G.A. Arteca, F.M. Fernández and E.A. Castro, Phys. Lett. A 36 (1981) 133.CrossRefGoogle Scholar
  18. /19/.
    A. Requena, R. Pena and A. Serna, An. Quim. 77 (1981) 231.Google Scholar
  19. /20/.
    E.J. Austin, Molec. Phys. 40 (1980) 893.CrossRefGoogle Scholar
  20. /21/.
    C.S. Lai, Phys. Lett. A 83 (1931) 322.CrossRefGoogle Scholar
  21. /22/.
    G.A. Arteca, F.M. Fernandez and E.A. Castro, Rev. Bras. Fis. 12 (1932) 766.Google Scholar
  22. /23/.
    G.A. Arteca, F.M. Fernandez and E.A. Castro, Chem. Phys. Lett. 92 (1932) 43.CrossRefGoogle Scholar
  23. /24/.
    A. Requena, R. Pena and A. Serna, Int. J. Quantum Chem. 17 (1930) 1931.Google Scholar
  24. /25/.
    F. M. Fernandez and E.A. Castro, J. Chem. Phys. 76 (1982) 525.CrossRefGoogle Scholar
  25. /26/.
    F. M. Fernandez and E.A. Castro, J. Mol. Spectrosc. 94 (1932) 23.Google Scholar
  26. /27/.
    A. Requena, R. Pena and J. Zflniga, J. Chem. Phys. 73 (1933) 4792.Google Scholar
  27. /28/.
    F. M. Fernandez and E.A. Castro, Match 15 (1984) 133.Google Scholar
  28. /29/.
    S. A. Maluendes, F.M. Fernandez and E.A. Castro, Match 16 (1984) 95.Google Scholar
  29. /30/.
    A. Requena, R. Pena and A. Serna, Int. J. Quantum Chem. 22 (1982) 1263.CrossRefGoogle Scholar
  30. /31/.
    F.M. Fernandez and E.A. Castro, Int. J. Quantum Chem. 19 (1981) 533.CrossRefGoogle Scholar
  31. /32/.
    S.A. Maluendes, F.M. Fernández and E.A. Castro, J.Mol. Spectrosc. 100 (1983) 24.CrossRefGoogle Scholar
  32. /33/.
    S.A. Maluendes, F.M. Fernandez and E.A. Castro, Phys. Rev. A 23 (1933) 2057.Google Scholar
  33. /34/.
    F.M. Fernández and E.A. Castro, Int. J. Quantum Chem. 19 (1981)521.CrossRefGoogle Scholar
  34. /35/.
    F.M. Fernandez and E.A. Castro, Int. J. Quantum Chem. 20 (1931)623.CrossRefGoogle Scholar
  35. /37/.
    F.M. Fernandez and E.A. Castro, Phys. Lett. A 88 (1982) 4.CrossRefGoogle Scholar
  36. /38/.
    F.M. Fernandez and E.A. Castro, Phys. Lett. A 24 (1981) 2883.Google Scholar
  37. /39/.
    G.A. Arteca, S.A. Maluendes, F.M. Fernandez and E.A. Castro, Phys. Lett. Int. J. Quantum Chem. 24 (1933). 169.CrossRefGoogle Scholar
  38. /40/.
    F.M. Fernandez and E.A. Castro, J. Math. Phys. 23 (1982) 1103.CrossRefGoogle Scholar
  39. /41/.
    F.M. Fernandez and E.A. Castro, J. Chem. Phys. 76 (1982) 2506.CrossRefGoogle Scholar
  40. /42/.
    G.A. Arteca, F.M. Fernandez and E.A. Castro, Z. Physik A 303 (1932). 115.Google Scholar
  41. /43/.
    F.M. Fernández and E.A. Castro, Physica A 111 (1932) 334.CrossRefGoogle Scholar
  42. /44/.
    G.A. Arteca, F.M. Fernandez and E.A. Castro, Nuevo Cimento B 72 (1932) 246.CrossRefGoogle Scholar
  43. /45/.
    F.M. Fernandez, A.M. Mesn and E.A. Castro, J. Math. Phys. 23 (1932) 254.CrossRefGoogle Scholar
  44. /46/.
    F.M. Fernandez and E.A. Castro, Kinam 8 (1982) 193.Google Scholar
  45. /47/.
    F.M. Fernandez, G.A. Arteca, S.A. Maluendes and E.A. Castro, J. Phys. A 15 (1982) 2123.CrossRefGoogle Scholar
  46. /48/.
    C.M. Bender and T.T. Wu, Phys. Rev. 134 (1969) 1231.CrossRefGoogle Scholar
  47. /49/.
    C.M. Bender, J. Math. Phys. 11 (1970) 796.CrossRefGoogle Scholar
  48. /50/.
    C.E. Solivérez and E. Gagliano, Chem: Phys. Lett. 91 (1982) 47.CrossRefGoogle Scholar
  49. /51/.
    V.S. Polikanov, Sov. Phys.-JETP 25 (1967) 882Google Scholar
  50. /52/.
    A.I. Mukhailov and V.S. Polikanov, Sov. Phys.-JET? 27 (1963) 95Google Scholar
  51. /53/.
    A.D. Dolgov and V.S. Popov, Phys,.Lett. B 79 (1973) 403.Google Scholar
  52. /54/.
    A.D. Dolgov and V.S. Popov, Phys. Lett. B 86 (1979) 185.CrossRefGoogle Scholar
  53. /55/.
    A.D. Dolgov and V.S. Popov, Sov. Phys.-JETP 43 (1973) 1012.Google Scholar
  54. /56/.
    V.L. Eletsky and V.S. Popov, Phys.Lett. B 94 (1930) 65.Google Scholar
  55. /57/.
    S.P. Alliluev, V.L. Eletskii, V.S. Popov and V.M. Vainberg, Phys. Lett. A 78 (1980) 43.CrossRefGoogle Scholar
  56. /58/.
    S.P. Alliluev, B.L. Eletskii, V.S. Popov and V.M. Vainberg, Sov. Phys. Dokl. 25 (1980) 851.Google Scholar
  57. /59/.
    A.L. Dolgov, V.L. Eletskii and V.S. Popov, Sov. Phys.-JETP 52 (1980) 861.Google Scholar
  58. /60/.
    Y. Aharonov and C.K. Au, Phys. Rev. Lett. 42 (1979) 1582.CrossRefGoogle Scholar
  59. /61/.
    Y. Aharonov and C.K. Au, Phys. Rev. A 20 (1979) 2245.CrossRefGoogle Scholar
  60. /62/.
    C.K. Au, Phys. Lett. A 77 (1980) 221.CrossRefGoogle Scholar
  61. /63/.
    A.V. Turbiner, JETP Lett. 30 (1979) 352.Google Scholar
  62. /64/.
    A.D. Dolgov and A.V. Turbiner, Phys. Lett. A 77 (1930) 15.CrossRefGoogle Scholar
  63. /65/.
    A.V. Turbiner, Sov. Phys.-JETP 52 (1980) 363.Google Scholar
  64. /66/.
    V. Privman, Phys. Rev. A 22 (1930) 1833.CrossRefGoogle Scholar
  65. /67/.
    V. Privman, Phys. Lett. A 31 (1981) 326.CrossRefGoogle Scholar
  66. /68/.
    A.V. Turbiner, JETP Lett. 33 (1931) 173.Google Scholar
  67. /69/.
    V.M. Vainberg, V.L. Eletskii and V.S. Popov, Sov. Phys.-JETP 54 (1981) 833.Google Scholar
  68. /70/.
    A.V. Turbiner, Preprint ITEP-79, Moscow, 1982.Google Scholar
  69. /71/.
    T. Imbo and M. Sukhatme, Am. J. Phys. 52 (1984) 140.CrossRefGoogle Scholar
  70. /72/.
    F.M. Fernandez and E.A. Castro, Int. J. Quantum Chem. 26 (1984) 497CrossRefGoogle Scholar
  71. /73/.
    F.M. Fernandez and E.A. Castro, Int. J. Quantum Chem. 28 (1984) 603.CrossRefGoogle Scholar
  72. /74/.
    F.L. Pilar, Elementary Quantum Chemistry, McGraw-Hill, New York, 1963.Google Scholar
  73. /75/.
    C.K. Au, G.W. Rogers and Y. Aharonov, Phys. Lett. A 95 (1983). 237.CrossRefGoogle Scholar
  74. /76/.
    J. Cizek and E.R. Vrscay, Int. J. Quantum Chem. 21 (1982) 27.CrossRefGoogle Scholar
  75. /77/.
    B.R. Johnson, K.F. Scheibner and D. Farrelly, Phys. Rev. Lett. 51 (1933) 2230.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • G. A. Arteca
    • 1
  • F. M. Fernández
    • 1
  • E. A. Castro
    • 1
  1. 1.División Química Teórica, Instituto de Investigaciones Fisicoquímicas, Teóricas y Aplicadas (INIFTA), Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina

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