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Variational Methods in Scattering Theory

  • Charles J. Joachain

Abstract

By writing the variational principle
$$\delta \boldsymbol{J} = 0$$
one expresses the fact that a certain functional J, characteristic of the system considered, is stationary for a “natural” system. This property leads to the well-known Euler-Lagrange equations of the system.

Keywords

Phase Shift Variational Principle Trial Function Born Approximation Scattering Theory 
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

  1. 1.
    L. Hulthén, Kgl. Fysiogr. Sallsk Lund Forh, 14(21): (1944).Google Scholar
  2. 2.
    I. G. Tamm, J. Exp. Theor. Phys. USSR., 14: 21 (1944).Google Scholar
  3. 3.
    J. Schwinger, unpublished lectures (1947); Phys. Rev., 72: 742 (1947).Google Scholar
  4. 4.
    L. Hulthen, Ark. Math. Ast. Phys. 35A (25): (1948).Google Scholar
  5. 5.
    W. Kohn, Phys. Rev. 74: 1763 (1948).ADSMATHCrossRefGoogle Scholar
  6. 6.
    J. M. Blatt and J. D. Jackson, Phys. Rev., 76: 18 (1949).ADSMATHCrossRefGoogle Scholar
  7. 7.
    B. A. Lippmann and J. Schwinger, Phys. Rev. 79: 469 (1950).MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    B. A. Lippmann, Phys. Rev. 102: 264 (1956).ADSMATHCrossRefGoogle Scholar
  9. 9.
    C. Joachain, Nucl. Phys. 64: 548 (1965).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    See, for example, H. S. W. Massey’s article in “Handbuch der Physik,” ed S. Flugge, 36: 285 (1956).Google Scholar
  11. 11.
    H. S. W. Massey and B. L. Moiseiwitsch, Proc. Roy. Soc. London A205: 483 (1950).ADSGoogle Scholar
  12. 12.
    B. L. Moiseiwitsch, Proc. Roy. Soc., London, A219: 102 (1953).ADSGoogle Scholar
  13. 13.
    S. S. Huang, Phys. Rev., 76: 477, 1878 (1949).ADSMATHCrossRefGoogle Scholar
  14. 14.
    C. Schwartz, Ann. Phys. (New York), 16: 36 (1961).ADSMATHCrossRefGoogle Scholar
  15. 15.
    C. Schwartz, Phys. Rev., 124: 1468 (1961).ADSCrossRefGoogle Scholar
  16. 16.
    M. L. Goldberger and K. M. Watson, “Collision Theory,” John Wiley, Inc., New York, 1964, p. 85.MATHGoogle Scholar
  17. 17.
    E. Gerjuoy and D. S. Saxon, Phys. Rev., 94: 484 (1954).MathSciNetADSGoogle Scholar
  18. 18.
    C. Joachain, Nucl. Phys. 64: 529 (1965).MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    C. Joachain, Ann. Inst. Henri Poincaré, 1: 55 (1964).MathSciNetGoogle Scholar
  20. 20.
    C. Joachain, Bull. Cl. Sc. Acad. Roy. Belg., 48: 302 (1962).Google Scholar
  21. 21.
    Y. Yamaguchi, Phys. Rev., 95: 1628 (1954).ADSMATHCrossRefGoogle Scholar
  22. 22.
    C. Schwartz, Phys. Rev. 141 (4): 1468 (1966).MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    C. Schwartz, and C. Zemach, Phys. Rev. 141 (4): 1454 (1966).MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    T. Kato, Progr. Theor. Phys., 6: 295 (1951).ADSMATHCrossRefGoogle Scholar
  25. 25.
    T. Kato, Progr. Theor. Phys. 6: 394 (1951).ADSMATHCrossRefGoogle Scholar
  26. 26.
    L. Spruch, “Minimum Principles in Scattering Theory,” Lectures in Theoretical Physics, Vol. IV, Interscience Publ. 1962, p. 161.Google Scholar
  27. 27.
    L. Spruch and L. Rosenberg, Phys. Rev., 116: 1034 (1959).MathSciNetADSMATHCrossRefGoogle Scholar
  28. 28.
    T. F. O’Malley, L. Spruch, and L. Rosenberg, J. Math. Phys. 2: 491 (1961).MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    L. Rosenberg, L. Spruch, and T. O’Malley, Phys. Rev., 118: 184 (1960).MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    L. Spruch and L. Rosenberg, Phys. Rev. 117: 1095 (1960).MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    L. Spruch and L. Rosenberg, Nucl. Phys. 17: 30 (1960).CrossRefGoogle Scholar
  32. 32.
    L. Spruch and L. Rosenberg, Phys. Rev. 117: 143 (1960).MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    L. Rosenberg, L. Spruch and T. F. O’Malley, Phys. Rev., 119: 164 (1960).MathSciNetADSMATHCrossRefGoogle Scholar
  34. 34.
    See, for example, Y. Hahn, and L. Spruch, phys. Rev. 153(4): 1159(1967); L. Rosenberg, Phys. Rev. B138: 1343 (1965).ADSCrossRefGoogle Scholar
  35. 35.
    R. Sugar and R. Blankenbecler, Phys. Rev., B136: 472 (1964).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Plenum Press 1968

Authors and Affiliations

  • Charles J. Joachain
    • 1
  1. 1.Department of Theoretical Physics and MathematicsUniversité Libre de BruxellesBrusselsBelgium

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