Skip to main content

Mathematical and Quantum-Mechanical Background

  • Chapter
Theory of Resonances

Part of the book series: Reidel Texts in the Mathematical Sciences ((RTMS,volume 3))

  • 383 Accesses

Abstract

In this book we shall use a number of mathematical methods which either are dealt with only in passing in the standard university mathematics course or are not treated at all; for example, the theory of divergent integrals and series, the Padé approximation method, and so on. Accounts of these problems may often be found only in monographs devoted to a narrow range of specialized problems or in original works. We shall also need the basic concepts and equations of the present-day quantum-mechanics theory of many-particle scattering, namely, the Faddeev-Yakubovsky equations which are not usually covered by the standard university courses on quantum mechanics. Therefore we have prefaced the main subject of the book by a concise account of complementary areas of mathematics and quantum scattering theory which provide an indispensable background for understanding the material to be presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hardy G. H., Divergent Series, 2nd ed., Clarendon Press, 1956

    Google Scholar 

  2. Zel’dovich Ya. B., ZhETF (in Russian) 39 (1960) 776 [Sov. Phys. JETP 12 (1961) 542].

    Google Scholar 

  3. Bateman H., Erdélyi A., Higher Transcedental Funstions, Vol. II, Mc Graw-Hill, N. Y.-To-ronto-London 1955.

    Google Scholar 

  4. Berggren T., Nucl. Phys. A109 (1968), 265.

    ADS  Google Scholar 

  5. Gyarmati B., Vertse T, Nucl. Phys. A160(1971) 523.

    MathSciNet  ADS  Google Scholar 

  6. Shnoll E. E., Theor. Math. Phys. (in Russian) 8 (1971) 140.

    Google Scholar 

  7. Baker G. A., Adv. in Theor. Phys. 1, ed. Brueckner, Academic Press, N. Y.-London 1965

    Google Scholar 

  8. Baker G. A., Baker G. A., Jr., Graves-Morris P., Padé Approximants, Encyclopedia of Mathematics and its Applications, V. 13, 14, G. C. Rota Ed., Addison-Wesley Publ. Co., 1981, London-Amsterdam

    Google Scholar 

  9. Basdevant J. L., Fortschritte der Physik 20 (1972) 283.

    Article  ADS  Google Scholar 

  10. Newton R. G., Scattering Theory of Waves and Particles, 2nd ed., Springer, Berlin, Heidelberg 1982.

    MATH  Google Scholar 

  11. Nuttal J., J. Math. Anal. Appl, 31 (1970) 147.

    Article  Google Scholar 

  12. Baker G. A., Gammel J. L., J. Math. Appl. 2 (1961) 21

    MathSciNet  MATH  Google Scholar 

  13. Zinn-Justin J., Phys. Rep. 10 (1971) 33.

    Google Scholar 

  14. Wall H. S., Analytic Theory of Continued Fractions; van Nostrand, Princeton, New Jersey 1948.

    MATH  Google Scholar 

  15. Schlessinger L., Phys. Rev. 167 (1968) 1411.

    Article  ADS  Google Scholar 

  16. Luke Y. L., Mathematical Functions and their Approximations, Academic Press, N. Y.-San Francisco-London 1975.

    MATH  Google Scholar 

  17. Hartt K., Phys. Rev. C22 (1980) 1377

    ADS  Google Scholar 

  18. Hartt K., Phys. Rev. C23 (1981) 2 399

    Google Scholar 

  19. Hartt K., Phys. Rev. C29 (1984) 695.

    MathSciNet  ADS  Google Scholar 

  20. Krasnopol’sky V. M., Kukulin V. L, Horáček J., Czech. J. Phys. B35 (1985) 805.

    Article  ADS  Google Scholar 

  21. Krasnopol’sky V. M., Chlebnikov S. Yu. in: Theory of Quantum Systems With Strong Interaction, Kalinin Univ., 1983, p. 80 (in Russian).

    Google Scholar 

  22. Baker G. A., Gammel J. L., The Padé Approximant in Theoretical Physics, Academic Press, N. Y. 1970.

    Google Scholar 

  23. Johnson R. C., New Theory of Padé Approximants, Preprint, Durham University 1971.

    Google Scholar 

  24. Loeffel J. J., Martin A., Simon B., Wightman A. S., Phys. Lett. 30B (1969) 656.

    ADS  Google Scholar 

  25. Smithies V, Integral Equations, Cambridge, New York. 1958.

    MATH  Google Scholar 

  26. Kloet W. M., Tjon J. A., Ann. Phys. 79 (1973) 407.

    Article  ADS  Google Scholar 

  27. Whittaker E. T., Watson G. N., A Course of Modern Analysis, Cambridge University Press, 1927.

    MATH  Google Scholar 

  28. Dienes P., The Taylor Series, Dover, New York 1957.

    MATH  Google Scholar 

  29. Pišút J., ECHaYa [Sov. J. Part. Nucl. 9 (1978) 246]. (in Russian) 9 (1978) No. 3, 602.

    Google Scholar 

  30. Yndurain F. J., CERN Preprint TH 1372, 1971, Yndurain F., Ann. Phys. 75 (1973) 171.

    Article  ADS  Google Scholar 

  31. Froissart M., Recherche Cooperative sur Programme, Prog. 25, Vol. 9, C.N.R.S., Strasbour 1969.

    Google Scholar 

  32. Wiener N., Cybernetics or Control and Communication in the Animal and the Machine. The technology press, N. Y.-Paris 1948.

    Google Scholar 

  33. Faddeev L. D., Zhetf (in Russian) 39 (1960) 1459 [Sov. Phys. JETP 12 (1961) 1014]; DAN USSR (ser. fiz.) (in Russian) 6 (1961) 384.

    MathSciNet  Google Scholar 

  34. Schmid E., Ziegelmann H., The Quantum Mechanical Three-Body Problem, Pergamon Press, Braunschweig 1974.

    Google Scholar 

  35. Baz A. L, Zel’dovich Ya. B., Perelomov A. M., Scattering, Reactions and Decay in Nonrelati-vistic Quantum Mechanics, Nauka, Moscow, 2nd ed. 1971 (in Russian). [English translation of 1st ed.: Israel Program for Scientific Translations, Jerusalem, 1966].

    Google Scholar 

  36. Sitenko A. G., The Lectures in the Scattering Theory (in Russian), Kiev 1971. [English translation: Pergamon Press, Oxford, 1971].

    Google Scholar 

  37. Fuller R. C., Phys. Rev. C3 (1971) 1 042.

    ADS  Google Scholar 

  38. Glöckle W., Heiss W. D., Nucl. Phys. A122 (1968) 343.

    ADS  Google Scholar 

  39. Riesz F., Szent-Nagy B., Leçons d’analyse fonctionelle, Budapest 1953.

    Google Scholar 

  40. Sasakawa T., Nucl. Phys. C160 (1971) 321.

    ADS  Google Scholar 

  41. Badalyan A. M., Simonov Yu. A., The Variational Method for the 3-body Resonances (Preprint series): I. The Asymptotic Behaviour of the Resonance Wave Function, Preprint ITEP No. 966, Moscow 1972

    Google Scholar 

  42. Badalyan A. M., Simonov Yu. A.,II. The Equation for the Resonance Wave Function, Preprint ITEP No. 952, Moscow 1972

    Google Scholar 

  43. Badalyan A. M., Simonov Yu. A.,Yad. Fiz. (in Russian) 17 (1973) 441 [Sov. J. Nucl. Phys. 17 (1973) 225].

    MathSciNet  Google Scholar 

  44. Weinberg S., Phys. Rev. 131 (1963) 440.

    Article  MathSciNet  ADS  Google Scholar 

  45. Merkuriev S. P., Faddeev L. D., Quantum-Mechanical Scattering Theory for Few Body Systems (in Russian) Nauka, Moscow 1985.

    Google Scholar 

  46. Narodetski I. M., Galpern E. S., Lyakhovitsky V. N., Yad. Fiz. (in Russian) 16 (1972) 707 [Sov. J. Nucl. Phys. 16 (1973) 395].

    Google Scholar 

  47. Belyaev V. B., Moller K., Preprint JINR E4–9601, Dubna 1976.

    Google Scholar 

  48. Harms E., Phys. Rev. D9 (1974) 993.

    MathSciNet  ADS  Google Scholar 

  49. Evgrafov M. A., Analytic Functions (in Russian), Nauka, Moscow 1968. [English translation: Saunders, Philadelphia, 1966].

    Google Scholar 

  50. Belyaev V. B., Lectures on Few Body Scattering Theory (in Russian), Energoizdat, Moscow 1985.

    Google Scholar 

  51. Goldberger M. L., Watson K. M., Collision Theory, Chap. 3, 8, John Wiley, N. Y.-London— Sydney 1964.

    Google Scholar 

  52. Baker G. A. Jr., Gammel J. L., Wills J. G., J. Math. Anal. Appl. 2 (1961) 405.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1989 V. I. Kukulin, V. M. Krasnopol’sky, J. Horáček

About this chapter

Cite this chapter

Kukulin, V.I., Krasnopol’sky, V.M., Horáček, J. (1989). Mathematical and Quantum-Mechanical Background. In: Theory of Resonances. Reidel Texts in the Mathematical Sciences, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7817-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-7817-2_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8432-3

  • Online ISBN: 978-94-015-7817-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics