Skip to main content

A two-Hilbert-space formulation of multi-channel scattering theory

  • Quantum-Mechanical Scattering Theory
  • Conference paper
  • First Online:
Mathematical Methods and Applications of Scattering Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 130))

  • 159 Accesses

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.O. Alt, P. Grassberger, W. Sandhas: Nucl. Phys. B2, 167 (1967)

    Google Scholar 

  2. W.O. Amrein, J.M. Jauch, K.B. Sinha: Scattering Theory in Quantum Mechanics (Benjamin, Reading, Massachusetts, 1977)

    Google Scholar 

  3. A.L. Belopol'skii, M. S. Birman: Math. USSR Izv. 2, 1117 (1968)

    Google Scholar 

  4. Gy. Bencze: Nucl. Phys. A210, 568 (1973)

    Google Scholar 

  5. Gy. Bencze: Phys. Lett. 72B, 155 (1977)

    Google Scholar 

  6. Gy. Bencze: Lett. Nuovo Cimento 17, 91 (1976)

    Google Scholar 

  7. Gy. Bencze, G. Cattapan, V. Vanzani: Lett. Nuovo Cimento 20, 248 (1977)

    Google Scholar 

  8. Gy. Bencze, C. Chandler: “On time dependent scattering theory for identical particles,” RIP Budapest, preprint KFKI-1979-14 (1979)

    Google Scholar 

  9. F.A. Berezin: Soviet Math. Dokl. 6, 997 (1965)

    Google Scholar 

  10. G. Cattapan, V. Vanzani: Nuovo Cimento 41A, 553 (1977)

    Google Scholar 

  11. C. Chandler, A.G. Gibson: J. Math, Phys. 14, 1328 (1973)

    Google Scholar 

  12. C. Chandler, A.G. Gibson: J. Math. Phys. 18, 2336 (1977)

    Google Scholar 

  13. C. Chandler, A.G. Gibson: J. Math. Phys. 19, 1610 (1978)

    Google Scholar 

  14. C. Chandler, A.G. Gibson: in Atomic Scattering Theory, Mathematical and Computational Aspects, ed. by J. Nuttall (University of Western Ontario, London, Canada, 1978), p. 189

    Google Scholar 

  15. C. Chandler, A.G. Gibson: in Few Body Systems and Nuclear Forces I, ed. by H. Zingl et al., Lecture Notes in Physics, Vol. 82 (Springer, New York, 1978), p. 356

    Google Scholar 

  16. F. Coester: Helv. Phys. Acta 38, 7 (1965)

    Google Scholar 

  17. F. Coester, L. Schlessinger: Ann. Phys. (N.Y.) 78, 90 (1973)

    Google Scholar 

  18. F. Coester: “Canonical scattering theory of relativistic particles,” these proceedings

    Google Scholar 

  19. J.M. Combes: Nuovo Cimento A64, 111 (1969)

    Google Scholar 

  20. P. Deift: Ph.D. thesis, Princeton University (1976)

    Google Scholar 

  21. J.D. Dollard: Rocky Mt. J. Math. 1, 5 (1971)

    Google Scholar 

  22. J.D. Dollard: J. Math Phys. 5, 729 (1964)

    Google Scholar 

  23. H. Ekstein: Phys. Rev. 101, 880 (1956)

    Google Scholar 

  24. D.E. Eyre, T.A. Osborn: “Cluster expansions of the three-body problem,” University of Manitoba preprint (1979)

    Google Scholar 

  25. L.D. Faddeev: in The Three-Body Problem, ed. by J.S.C. McKee, P. M. Rolph, (North-Holland, Amsterdam, 1970), p. 154

    Google Scholar 

  26. L.D. Faddeev: Mathematical Aspects of the Three-Body Problem in Quantum Scattering Theory (Israel Program for Scientific Translations, Jerusalem, 1965)

    Google Scholar 

  27. J. Ginibre, M. Moulin: Ann. Inst. Henri Poincaré 21, 97 (1974)

    Google Scholar 

  28. R. Goldflam, K.L. Kowalski, W. Tobocman: “Partition permuting array approach to few-body Hamiltonian models of nuclear reactions,” Case Western Reserve University preprint (1979)

    Google Scholar 

  29. P. Grassberger, W. Sandhas: Nucl. Phys. B2, 181 (1967)

    Google Scholar 

  30. K. Gustafson, in Operator Algebras, Ideals, and Their Applications in Theoretical Physics, ed. by H. Baumgärtel et al. (Teubner-Texte, Leipzig, 1978), p. 335

    Google Scholar 

  31. G.A. Hagedorn: Ph. D. thesis, Princeton University (1978)

    Google Scholar 

  32. J. S. Howland: J. Functional Anal. 22, 250 (1976)

    Google Scholar 

  33. W. Hunziker, in Lectures in Theoretical Physics, ed. by A.O. Barut, W.E. Britten (Gordon and Breach, New York, 1968), Vol. X–A

    Google Scholar 

  34. W. Hunziker: Helv. Phys. Acta 40, 1052 (1967)

    Google Scholar 

  35. J.M. Jauch: Helv. Phys. Acta 31, 127, 661 (1958)

    Google Scholar 

  36. B.R. Karlsson, E. M. Zeiger: Phys. Rev. D 11, 939 (1975);,D 16, 2553 (1977)

    Google Scholar 

  37. T. Kato: Perturbation Theory for Linear Operators, (Springer, New York, 1976), 2nd ed.

    Google Scholar 

  38. T. Kato: J. Functional Anal. 1, 342 (1967)

    Google Scholar 

  39. D.J. Kouri, F. S. Levin: Nucl. Phys. A250, 127 (1975)

    Google Scholar 

  40. H. Krüger, F. S. Levin: Phys. Lett. 65B, 109 (1976)

    Google Scholar 

  41. S.P. Merkuriev: Sov. J. Nucl. Phys. 24, 150 (1976)

    Google Scholar 

  42. S.P. Merkuriev: Theoret. Math. Phys. 32, 680 (1977)

    Google Scholar 

  43. S.P. Merkuriev: Teoret. Mat. Fiz. 38, 201 (1979); Lett. Math. Phys. 3, 141 (1979)

    Google Scholar 

  44. I.M. Narodetskii, O.A. Yakubovskii: Sov. J. Nucl. Phys. 14, 178 (1972)

    Google Scholar 

  45. T.A. Osborn, K.L. Kowalski: Ann. Phys. (N. Y.) 68, 36 (1971)

    Google Scholar 

  46. D.B. Pearson: J. Functional Anal. 28, 182 (1978)

    Google Scholar 

  47. W.V. Petryshyn: Bull. Am. Math. Soc. 81, 223 (1975); Proc. Sympos. Pure Math. 18, part 1 (Am. Math. Soc., Providence, Rhode Island, 1970), p. 206

    Google Scholar 

  48. W.N. Polyzou, E.F. Redish: Ann. Phys. (N.Y.), 119, 1 (1979)

    Google Scholar 

  49. E.F. Redish: Nucl. Phys. A225, 16 (1974)

    Google Scholar 

  50. M. Reed, B. Simon: Methods of Modern Mathematical Physics, Vol. III (Academic, New York, 1979)

    Google Scholar 

  51. I.M. Sigal: Comm. Math. Phys. 48, 137 (1976)

    Google Scholar 

  52. B. Simon: Comm. Math. Phys. 55, 259 (1977)

    Google Scholar 

  53. I.H. Sloan: Phys. Rev. C 6, 1945 (1972)

    Google Scholar 

  54. W. Tobocman: Phys. Rev. C 11, 43 (1975)

    Google Scholar 

  55. T.G. Trucano: Ph. D. thesis, University of New Mexico, in progress

    Google Scholar 

  56. C. van Winter: Mat. Fys. Skr. Dan. Vid. Selsk. 2, 1 (1964)

    Google Scholar 

  57. V. Vanzani: in Few-Body Nuclear Physics (IAEA, Vienna, 1978), p. 57

    Google Scholar 

  58. S. Weinberg: Phys. Rev. 133, B232 (1964)

    Google Scholar 

  59. C.H. Wilcox: J. Functional Anal. 12, 257 (1973)

    Google Scholar 

  60. O.A. Yakubovskii: Sov. J. Nucl. Phys. 5, 937 (1967)

    Google Scholar 

  61. W.W. Zachary: J. Math. Phys. 10, 1098 (1969)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

John A. DeSanto Albert W. Sáenz Woodford W. Zachary

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Chandler, C., Gibson, A.G. (1980). A two-Hilbert-space formulation of multi-channel scattering theory. In: DeSanto, J.A., Sáenz, A.W., Zachary, W.W. (eds) Mathematical Methods and Applications of Scattering Theory. Lecture Notes in Physics, vol 130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10023-7_106

Download citation

  • DOI: https://doi.org/10.1007/3-540-10023-7_106

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10023-2

  • Online ISBN: 978-3-540-38184-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics